Chapter 8 - Time Value of Money TRUE/FALSE 1. Starting to invest early for retirement increases the benefits of compound interest. ANS: T PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 2. Starting to invest early for retirement reduces the benefits of compound interest. ANS: F PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 3. A time line is meaningful even if all cash flows do not occur annually. ANS: T PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 4. A time line is not meaningful unless all cash flows occur annually. ANS: F PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 5. Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly. ANS: T PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 6. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. ANS: F PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 7. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. ANS: T PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 8. Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods. ANS: F PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 9. Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts. ANS: T PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 10. Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts. ANS: F PTS: 1 DIF: EASY NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 11. If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series. ANS: F PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 12. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. ANS: T PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 13. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value. ANS: T PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 14. Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value. ANS: F PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 15. If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate. ANS: F PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 16. If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate. ANS: T PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 17. The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date. ANS: F PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 18. The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date. ANS: T PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 19. Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.) ANS: T Work out the numbers with a calculator: PV 1000 FV A = $1,710.34 Rate on A 5% 2FV A = $3,420.68 Rate on B 12% FV B = $3,478.55 Years 11 FV B > 2FV A, so TRUE PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 20. Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.) ANS: F Work out the numbers with a calculator: PV 1000 FV A = $1,710.34 Rate on A 5% 2FV A = $3,420.68 Rate on B 12% FV B = $3,478.55 Years 11 FV B > 2FV A, so FALSE PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 21. The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant. ANS: T PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 22. The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant. ANS: F PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 23. All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases. ANS: T One could make up an example and see that the statement is true. Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 24. All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases. ANS: F One could make up an example and see that the statement is false. Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 25. If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year. ANS: T PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 26. If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year. ANS: F PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 27. As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan). ANS: T PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 28. As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan). ANS: F PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 29. When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years. ANS: F PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 30. When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage increases in the loan's later years. ANS: T PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 31. The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal. ANS: T PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 32. The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal. ANS: F PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 33. Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan. ANS: F There is no reason to think that this statement would always be true. The portion of the representing interest declines, while the portion representing principal repayment increases. Therefore, the statement is false. We could also work out some numbers to prove this point. Here's an example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is not equal to the principal repayment component except at the high interest rate. Original loan Rate Life Payment 1 2 3 $1,000 10% 3 $402.11 Ending Beg. Interest Principal Bal. Balance $1,000.00 $100.00 $302.11 $697.89 1 $697.89 $69.79 $332.33 $365.56 2 $365.56 $36.56 $365.56 $0.00 3 Original loan $1,000 Rate 41.45% Life 3 Payment $640.98 Beg. Ending Balance Interest Principal Bal. $1,000.00 $414.50 $773.52 $320.62 $453.15 $187.83 $226.48 $320.36 $453.15 $773.52 $453.15 $0.00 PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 34. Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal. The proportions depend on the original life of the loan and the interest rate. ANS: T This statement is true. The portion of the payment representing interest declines, while the portion representing principal repayment increases. The interest portion could be equal to, greater than, or less than the principal portion. We can work out some numbers to prove this point. Here's an example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is less than the principal at 10%, equal at about 41.45%, and greater at rates above 41.45%. Original loan $1,000 Original loan $1,000 Rate Life Payment 10% 3 $402.11 Ending Interest Principal Bal. Rate Life Payment Beg. Balance Beg. Balance 1 $1,000.00 $100.00 $302.11 $697.89 1 $1,000.00 2 $697.89 $69.79 $332.33 $365.56 2 $773.52 3 $365.56 $36.56 $365.56 $0.00 3 $453.15 41.45% 3 $640.98 Ending Interest Principal Bal. $414.50 $226.48 $320.62 $320.36 $187.83 $453.15 $773.52 $453.15 $0.00 PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. MULTIPLE CHOICE 1. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. d. Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods. e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts. ANS: B PTS: 1 DIF: MEDIUM NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 2. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts. ANS: D PTS: 1 DIF: MEDIUM NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 3. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. e. Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity. ANS: C PTS: 1 DIF: MEDIUM NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 4. Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. e. Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity. ANS: E PTS: 1 DIF: MEDIUM NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 5. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment? a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000. b. The discount rate increases. c. The riskiness of the investment's cash flows decreases. d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years. e. The discount rate decreases. ANS: B PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 6. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment? a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for 10 years rather than 5 years, hence that each payment is for $10,000 rather than for $20,000. b. The discount rate decreases. c. The riskiness of the investment's cash flows increases. d. The total amount of cash flows remains the same, but more of the cash flows are received in the later years and less are received in the earlier years. e. The discount rate increases. ANS: B PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 7. Which of the following statements is CORRECT? a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity. c. The cash flows for an annuity due must all occur at the ends of the periods. d. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month. e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity. ANS: D PTS: 1 DIF: MEDIUM NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 8. Which of the following statements is CORRECT? a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity. c. The cash flows for an annuity due must all occur at the beginning of the periods. d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month. e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity. ANS: C PTS: 1 DIF: MEDIUM NAT: Reflective thinking LOC: Students will acquire an understanding of the time value of money. 9. Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? a. The periodic rate of interest is 1.5% and the effective rate of interest is 3%. b. The periodic rate of interest is 6% and the effective rate of interest is greater than 6%. c. The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%. d. The periodic rate of interest is 3% and the effective rate of interest is 6%. e. The periodic rate of interest is 6% and the effective rate of interest is also 6%. ANS: C PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 10. Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? a. The periodic rate of interest is 2% and the effective rate of interest is 4%. b. The periodic rate of interest is 8% and the effective rate of interest is greater than 8%. c. The periodic rate of interest is 4% and the effective rate of interest is less than 8%. d. The periodic rate of interest is 2% and the effective rate of interest is greater than 8%. e. The periodic rate of interest is 8% and the effective rate of interest is also 8%. ANS: D PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 11. A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan. c. The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower. d. The last payment would have a higher proportion of interest than the first payment. e. The proportion of interest versus principal repayment would be the same for each of the 7 payments. ANS: C PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 12. A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan. c. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower. d. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher. e. The proportion of interest versus principal repayment would be the same for each of the 7 payments. ANS: D PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 13. Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) a. The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. b. Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant. c. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant. d. The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year. e. The outstanding balance declines at a slower rate in the later years of the loan ANS: B PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 14. Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) a. The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. b. Because the outstanding balance declines over time, the monthly payments will also decline over time. c. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant. d. The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year. e. The outstanding balance declines at a faster rate in the later years of the loan ANS: E PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 15. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? a. The monthly payments will decline over time. b. A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment. c. The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity. d. The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%. e. Exactly 10% of the first monthly payment represents interest. ANS: B PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 16. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? a. The monthly payments will increase over time. b. A larger proportion of the first monthly payment will be interest, and a smaller proportion will be principal, than for the last monthly payment. c. The total dollar amount of interest being paid off each month gets larger as the loan approaches maturity. d. The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%. e. Exactly 10% of the first monthly payment represents interest. ANS: B PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 17. Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero. a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments). b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments). c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). d. Investment D pays $2,500 at the end of 10 years (just one payment). e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments). ANS: A A dominates B because it provides the same total amount, but it comes faster, hence it can earn more interest over the 10 years. A also dominates C and E for the same reason, and it dominates D because with D no interest whatever is earned. We could also do these calculations to answer the question: A $4,382.79 Largest EFF% 10.00% 10 250 B $4,081.59 NOM% 9.76% 125 C $4,280.81 125 D $2,500.00 2500 E $3,984.36 250 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 18. Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero. a. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments). b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments). c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). d. Investment D pays $2,500 at the end of 10 years (just one payment). e. Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments). ANS: D A is smaller than E and B is smaller than C because the money comes in later. A is smaller than B because a larger annuity is received later. So, now the choice comes down to either A or D. Since all of D is received at the end, this is the logical choice. We could also do these calculations to answer the question: A B C D E $1,536.14 EFF% $1,573.63 NOM% $1,650.44 $963.86 SMALLEST $1,689.76 10.00% 9.76% 10 250 125 125 2500 250 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 19. A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT? a. The periodic interest rate is greater than 3%. b. The periodic rate is less than 3%. c. The present value would be greater if the lump sum were discounted back for more periods. d. The present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually. e. The PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity. ANS: D PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 20. A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT? a. The periodic interest rate is greater than 3%. b. The periodic rate is less than 3%. c. The present value would be greater if the lump sum were discounted back for more periods. d. The present value of the $1,000 would be larger if interest were compounded monthly rather than semiannually. e. The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity. ANS: E PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 21. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant? a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity. b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage. c. A bank loan's nominal interest rate will always be equal to or less than its effective annual rate. d. If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%. e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit. ANS: C PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 22. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant? a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity. b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage. c. A bank loan's nominal interest rate will always be equal to or greater than its effective annual rate. d. If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%. e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit. ANS: D PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 23. Which of the following statements is CORRECT? a. The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity. b. If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%. c. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different. d. The proportion of the payment that goes toward interest on a fully amortized loan increases over time. e. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%. ANS: A PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 24. Which of the following statements is CORRECT? a. The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due. b. If a loan has a nominal annual rate of 8%, then the effective rate will never be less than 8%. c. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different. d. The proportion of the payment that goes toward interest on a fully amortized loan increases over time. e. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%. ANS: B PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 25. You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT? a. The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE. b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD. c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. d. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD. e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant. ANS: D PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 26. You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT? a. A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ. b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD. c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. d. The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD. e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant. ANS: A PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 27. Which of the following statements is CORRECT? a. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0. b. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost. c. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial calculator but quite difficult otherwise. d. If you solve for I and get a negative number, then you must have made a mistake. e. If CF0 is positive and all the other CFs are negative, then you cannot solve for I. ANS: C PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 28. Which of the following statements is CORRECT? a. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0. b. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost. c. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the FV of the negative CFs. It is impossible to find the value of I without a computer or financial calculator. d. If you solve for I and get a negative number, then you must have made a mistake. e. If CF0 is positive and all the other CFs are negative, then you can still solve for I. ANS: E PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 29. Which of the following bank accounts has the highest effective annual return? a. An account that pays 8% nominal interest with monthly compounding. b. An account that pays 8% nominal interest with annual compounding. c. An account that pays 7% nominal interest with daily (365-day) compounding. d. An account that pays 7% nominal interest with monthly compounding. e. An account that pays 8% nominal interest with daily (365-day) compounding. ANS: E PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 30. Which of the following bank accounts has the lowest effective annual return? a. An account that pays 8% nominal interest with monthly compounding. b. An account that pays 8% nominal interest with annual compounding. c. An account that pays 7% nominal interest with daily (365-day) compounding. d. An account that pays 7% nominal interest with monthly compounding. e. An account that pays 8% nominal interest with daily (365-day) compounding. ANS: D PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 31. You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest? a. Bank 1; 6.1% with annual compounding. b. Bank 2; 6.0% with monthly compounding. c. Bank 3; 6.0% with annual compounding. d. Bank 4; 6.0% with quarterly compounding. e. Bank 5; 6.0% with daily (365-day) compounding. ANS: E PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 32. Sue now has $490. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding? a. $941.10 b. $724.64 c. $837.58 d. $1,148.14 e. $1,157.55 ANS: A N I/YR PV PMT 8 8.5% $490 $0 FV $941.10 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 33. Jose now has $500. How much would he have after 6 years if he leaves it invested at 7.5% with annual compounding? a. $679.05 b. $763.93 c. $910.55 d. $879.68 e. $771.65 ANS: E N I/YR PV PMT FV 6 7.5% $500 $0 $771.65 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 34. Suppose you have $1,425 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures? a. $1,810.92 b. $1,692.45 c. $1,827.85 d. $2,047.87 e. $1,709.38 ANS: B N I/YR PV PMT FV 5 3.5% $1,425 $0 $1,692.45 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 35. Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 4.0% interest, compounded annually. How much will you have when the CD matures? a. $2,516.42 b. $2,960.49 c. $3,641.40 d. $3,019.70 e. $2,634.83 ANS: B N I/YR PV PMT 10 4.0% $2,000 $0 FV $2,960.49 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 36. Last year Rocco Corporation's sales were $725 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later? a. $756.77 b. $1,096.34 c. $1,212.77 d. $921.70 e. $970.21 ANS: E N I/YR PV PMT FV 5 6.0% $725.00 $0.00 $970.21 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 37. Last year Dania Corporation's sales were $525 million. If sales grow at 7.0% per year, how large (in millions) will they be 8 years later? a. $1,028.33 b. $757.72 c. $793.80 d. $1,109.52 e. $902.05 ANS: E N I/YR PV PMT FV 8 7.0% $525.00 $0.00 $902.05 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 38. How much would $1, growing at 8.5% per year, be worth after 75 years? a. $426.93 b. $563.19 c. $454.18 d. $413.31 e. $449.64 ANS: C N I/YR PV PMT FV 75 8.5% $1.00 $0.00 $454.18 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 39. How much would $100, growing at 5% per year, be worth after 20 years? a. $254.72 b. $286.56 c. $265.33 d. $281.25 e. $331.66 ANS: C N I/YR PV PMT FV 20 5.0% $100.00 $0.00 $265.33 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 40. You deposit $825 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years? a. $1,949.68 b. $2,242.13 c. $1,969.17 d. $1,637.73 e. $2,008.17 ANS: A N I/YR PV PMT FV 25 3.5% $825 $0 $1,949.68 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 41. You deposit $500 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 10 years? a. $867.52 b. $705.30 c. $599.50 d. $613.61 e. $733.51 ANS: B N I/YR PV PMT FV 10 3.5% $500 $0 $705.30 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 42. Suppose a State of New York bond will pay $1,000 ten years from now. If the going interest rate on these 10-year bonds is 4.1%, how much is the bond worth today? a. $669.10 b. $675.79 c. $628.96 d. $749.39 e. $649.03 ANS: A N I/YR PMT FV PV 10 4.1% $0 $1,000.00 $669.10 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 43. Suppose a State of California bond will pay $1,000 eight years from now. If the going interest rate on these 8-year bonds is 7.3%, how much is the bond worth today? a. $478.06 b. $631.72 c. $569.12 d. $500.82 e. $529.28 ANS: C N I/YR PMT FV PV 8 7.3% $0 $1,000.00 $569.12 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 44. How much would $15,000 due in 50 years be worth today if the discount rate were 7.5%? a. $488.04 b. $310.57 c. $463.84 d. $403.34 e. $395.27 ANS: D N I/YR PMT FV PV PTS: 1 50 7.5% $0 $15,000 $403.34 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 45. How much would $5,000 due in 100 years be worth today if the discount rate were 5.5%? a. $21.75 b. $27.66 c. $20.81 d. $25.77 e. $23.64 ANS: E N I/YR PMT FV PV 100 5.5% $0 $5,000 $23.64 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 46. Suppose a U.S. treasury bond will pay $2,875 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today? a. $2,334.84 b. $2,428.24 c. $2,124.71 d. $2,381.54 e. $2,918.55 ANS: A N I/YR PMT FV PV 5 4.25% $0 $2,875.00 $2,334.84 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 47. Suppose an Exxon Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 6.00%, how much is the bond worth today? a. $2,990.20 b. $2,512.78 c. $1,934.84 d. $2,814.31 e. $3,090.72 ANS: B N I/YR PMT FV PV 10 6.00% $0 $4,500.00 $2,512.78 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 48. Suppose the U.S. Treasury offers to sell you a bond for $547.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price? a. 13.84% b. 12.17% c. 11.66% d. 11.40% e. 12.81% ANS: E N PV PMT FV I/YR 5 $547.25 $0 $1,000.00 12.81% PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 49. Suppose the U.S. Treasury offers to sell you a bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $4,600. What interest rate would you earn if you bought this bond at the offer price? a. 3.58% b. 4.32% c. 4.37% d. 5.46% e. 4.11% ANS: C N PV PMT FV I/YR 10 $3,000.00 $0 $4,600.00 4.37% PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 50. Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this year were $6.20. What was the growth rate in earnings per share (EPS) over the 10-year period? a. 26.91% b. 27.77% c. 28.63% d. 21.76% e. 29.78% ANS: C N PV PMT FV I/YR 10 $0.50 $0 $6.20 28.63% PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 51. Five years ago, Weed Go Inc. earned $1.20 per share. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period? a. 21.67% b. 26.66% c. 22.76% d. 20.59% e. 20.81% ANS: A N PV PMT FV I/YR 5 $1.20 $0 $3.20 21.67% PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 52. Janice has $5,000 invested in a bank that pays 5.2% annually. How long will it take for her funds to triple? a. 25.36 years b. 21.67 years c. 26.22 years d. 19.72 years e. 20.59 years ANS: B I/YR PV PMT FV N 5.2% $5,000.00 $0 $15,000.00 21.67 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 53. Bob has $2,500 invested in a bank that pays 1% annually. How long will it take for his funds to double? a. 74.54 years b. 79.41 years c. 73.14 years d. 69.66 years e. 84.99 years ANS: D I/YR PV PMT FV N 1.0% $2,500.00 $0 $5,000.00 69.66 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 54. Last year Thomson Inc's earnings per share were $3.50, and its growth rate during the prior 5 years was 12.0% per year. If that growth rate were maintained, how many years would it take for Thomson's EPS to triple? a. 9.69 b. 9.11 c. 11.25 d. 10.86 e. 10.76 ANS: A I/YR PV PMT FV N 12.0% $3.50 $0 $10.50 9.69 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 55. You plan to invest in securities that pay 6.2%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20? a. 8.82 b. 7.92 c. 11.63 d. 10.03 e. 11.53 ANS: D I/YR PV PMT FV N 6.2% $5,000.00 $0 $9,140.20 10.03 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 56. You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $25,000? a. 15.41 b. 18.08 c. 17.77 d. 15.73 e. 14.31 ANS: D I/YR PV PMT 6.0% $10,000.00 $0 FV N $25,000.00 15.73 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 57. You want to buy a new sports car 3 years from now, and you plan to save $7,400 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now? a. $26,646.83 b. $19,400.76 c. $24,776.87 d. $23,374.41 e. $22,205.69 ANS: D N I/YR PV PMT FV 3 5.2% $0.00 $7,400 $23,374.41 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 58. You want to buy a new ski boat 2 years from now, and you plan to save $5,400 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now? a. $10,133 b. $11,135 c. $12,582 d. $10,467 e. $13,139 ANS: B N I/YR PV PMT FV 2 6.2% $0.00 $5,400 $11,135 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 59. You want to go to Europe 5 years from now, and you can save $8,700 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now? a. $56,190.31 b. $63,922.92 c. $40,209.58 d. $41,756.10 e. $51,550.74 ANS: E N I/YR PV PMT FV 5 8.5% $0.00 $8,700 $51,550.74 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 60. You want to quit your job and go back to school for a law degree 4 years from now, and you plan to save $6,400 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today? a. $22,980.31 b. $22,685.69 c. $26,221.12 d. $29,461.93 e. $31,524.26 ANS: D BEGIN Mode N 4 I/YR 5.7% PV $0.00 PMT $6,400 FV $29,461.93 0 $6,400 1 $6,400 Alternative setup: 2 3 4 $6,400 $6,400 FV = $29,461.93 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 61. You want to quit your job and return to school for an MBA degree 3 years from now, and you plan to save $5,900 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today? a. $19,605.44 b. $17,840.95 c. $23,330.48 d. $19,801.50 e. $21,173.88 ANS: A BEGIN Mode N 3 I/YR 5.2% PV $0.00 PMT $5,900 FV $19,605.44 0 $5,900 1 $5,900 Alternative setup: 2 3 $5,900 $5,900 FV = $19,605.44 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 62. What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%? a. $15,467.21 b. c. d. e. $24,625.42 $17,705.88 $17,909.40 $20,351.59 ANS: E N I/YR PMT FV PV 10 5.5% $2,700 $0.00 $20,351.59 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 63. What is the PV of an ordinary annuity with 5 payments of $17,700 if the appropriate interest rate is 4.5%? a. $91,689.05 b. $87,026.90 c. $61,385.04 d. $77,702.59 e. $68,378.28 ANS: D N I/YR PMT FV PV 5 4.5% $17,700 $0.00 $77,702.59 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 64. You have a chance to buy an annuity that pays $12,800 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. $42,821.60 b. $27,972.17 c. $43,166.93 d. $39,022.91 e. $34,533.55 ANS: E N I/YR PMT FV PV 3 5.5% $12,800 $0.00 $34,533.55 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 65. You just inherited some money, and a broker offers to sell you an annuity that pays $5,200 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. $55,731.00 b. $74,524.02 c. $64,803.49 d. $60,267.25 e. $69,987.77 ANS: C N I/YR PMT FV PV 20 5.0% $5,200 $0.00 $64,803.49 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 66. Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $40,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today? a. $503,512.37 b. $571,292.88 c. $455,097.72 d. $484,146.51 e. $561,609.95 ANS: D N 30 I/YR 7.25% PMT $40,000 FV $0.00 PV $484,146.51 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 67. What is the PV of an annuity due with 5 payments of $5,400 at an interest rate of 5.5%? a. $20,921.92 b. $25,544.20 c. $24,327.81 d. $27,976.98 e. $25,787.48 ANS: C BEGIN Mode N 5 I/YR 5.5% PMT $5,400 FV $0.00 PV $24,327.81 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 68. What's the present value of a perpetuity that pays $3,800 per year if the appropriate interest rate is 5%? a. $76,000.00 b. $90,440.00 c. $92,720.00 d. $71,440.00 e. $63,840.00 ANS: A I/YR PMT PV 5.0% $3,800 $76,000.00 PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 69. What's the rate of return you would earn if you paid $3,680 for a perpetuity that pays $85 per year? a. 2.01% b. 1.99% c. 2.73% d. 2.15% e. 2.31% ANS: E Cost (PV) PMT I/YR $3,680 $85 2.31% PTS: 1 DIF: EASY NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 70. You have a chance to buy an annuity that pays $2,350 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. $6,688.85 b. $7,090.18 c. $7,825.96 d. $6,822.63 e. $6,956.41 ANS: A BEGIN Mode N 3 I/YR 5.5% PMT $2,350 FV $0.00 PV $6,688.85 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 71. You have a chance to buy an annuity that pays $28,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. $128,450.72 b. $118,174.66 c. $120,743.68 d. $129,735.23 e. $98,907.05 ANS: A BEGIN Mode N 5 I/YR 4.5% PMT $28,000 FV $0.00 PV $128,450.72 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 72. Your uncle is about to retire, and he wants to buy an annuity that will provide him with $73,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today? a. $1,059,405.81 b. $712,520.72 c. $937,527.27 d. $918,776.72 e. $975,028.36 ANS: C BEGIN Mode N 20 I/YR 5.25% PMT $73,000 FV $0.00 PV $937,527.27 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 73. Your father is about to retire, and he wants to buy an annuity that will provide him with $91,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today? a. $1,248,843.27 b. $1,408,270.07 c. $1,474,697.91 d. $1,328,556.67 e. $1,169,129.87 ANS: D BEGIN Mode N 25 I/YR PMT FV PV 5.15% $91,000 $0.00 $1,328,556.67 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 74. You inherited an oil well that will pay you $30,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it? a. $269,616.75 b. $294,780.98 c. $348,704.33 d. $359,489.00 e. $399,032.79 ANS: D BEGIN Mode N 25 I/YR 7.5% PMT $30,000 FV $0.00 PV $359,489.00 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 75. Sam was injured in an accident, and the insurance company has offered him the choice of $49,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity? a. $437,070.42 b. $576,560.98 c. $506,815.70 d. $427,771.05 e. $464,968.53 ANS: E BEGIN Mode N 15 I/YR 7.5% PMT $49,000 FV $0.00 PV $464,968.53 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 76. What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $2,950 at the end of Year 4 if the interest rate is 5%? a. $11,133.74 b. $8,740.50 c. $10,405.36 d. $8,532.40 e. $12,590.49 ANS: C N I/YR PMT FV PV 4 5.0% $2,250 $2,950 $10,405.36 PV = 0 1 $2,250 $2,250 Alternative setup: 3 4 $2,250 $2,250 $3,000 $2,250 $2,250 $5,250 2 $2,250 $10,405.36 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 77. Suppose you inherited $630,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years? a. $49,023.94 b. $65,365.26 c. $81,052.92 d. $79,745.61 e. $81,706.57 ANS: B N 20 I/YR 8.25% PV $630,000 FV $0.00 PMT $65,365.26 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 78. Your uncle has $1,135,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account? a. $98,766.96 b. $93,675.88 c. $92,657.67 d. $101,821.61 e. $120,149.50 ANS: D N 25 I/YR 7.5% PV $1,135,000 FV $0.00 PMT $101,821.61 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 79. Your uncle has $1,025,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account? a. $85,538.08 b. $65,864.32 c. $88,104.22 d. $103,501.08 e. $73,562.75 ANS: A BEGIN Mode N 25 I/YR 7.5% PV $1,025,000 FV $0.00 PMT $85,538.08 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 80. Your grandmother just died and left you $132,500 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account? a. $37,769.20 b. $39,221.86 c. $37,406.03 d. $33,774.38 e. $36,316.54 ANS: E BEGIN Mode N 4 I/YR 6.5% PV $132,500 FV $0.00 PMT $36,316.54 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 81. Suppose you inherited $870,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years? a. $67,543.38 b. $76,715.94 c. $99,230.40 d. $83,386.89 e. $97,562.66 ANS: D BEGIN Mode N 20 I/YR 8.25% PV $870,000 FV PMT $0.00 $83,386.89 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 82. Your father's employer was just acquired, and he was given a severance payment of $397,500, which he invested at a 7.5% annual rate. He now plans to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero? a. 27.19 b. 24.55 c. 26.13 d. 21.38 e. 26.40 ANS: E I/YR PV PMT FV N 7.5% $397,500 $35,000 $0.00 26.40 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 83. Your uncle has $280,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end? a. 10.31 b. 13.39 c. 15.67 d. 15.80 e. 14.19 ANS: B I/YR PV PMT FV N 7.50% $280,000 $35,000 $25,000 13.39 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 84. Your Aunt Ruth has $450,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i.e., run the account down to zero? a. 13.82 b. 15.11 c. 23.03 d. 15.29 e. 18.43 ANS: E BEGIN Mode I/YR 6.5% PV $450,000 PMT $40,000 FV $0.00 N 18.43 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 85. Your aunt has $760,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end? a. 41.13 b. 39.50 c. 40.72 d. 39.10 e. 45.61 ANS: C BEGIN Mode I/YR 5.5% PV $760,000 PMT $45,000 FV $50,000 N 40.72 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 86. Suppose you just won the state lottery, and you have a choice between receiving $2,075,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes. a. 11.10% b. 10.38% c. 12.14% d. 9.44% e. 11.83% ANS: B N PV PMT FV I/YR 20 $2,075,000 $250,000 $0.00 10.38% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 87. Your girlfriend just won the Florida lottery. She has the choice of $16,600,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity? a. 2.75% b. 2.73% c. 2.52% d. 2.35% e. 2.54% ANS: D N 20 PV $16,600,000 PMT $1,050,000 FV $0.00 I/YR 2.35% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 88. Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to start a new business, and your uncle offers to give you $80,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment? a. 23.15% b. 16.17% c. 20.96% d. 19.96% e. 22.16% ANS: D BEGIN Mode N 12 PV $80,000 PMT $15,000 FV $0.00 I/YR 19.96% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 89. What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $2,500? a. $138.13 b. $191.75 c. $144.63 d. $199.88 e. $162.50 ANS: E Cost (PV) I/YR PMT $2,500 6.5% $162.50 Multiply Cost by I/YR. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 90. What is the present value of the following cash flow stream at a rate of 16.00%? Years: 0 CFs: $0 a. b. c. d. e. 1 $75 2 $225 3 $0 4 $300 $397.55 $441.29 $322.02 $401.53 $469.11 ANS: A I/YR = 16.00% 0 $0 $0 1 $75 $65 2 $225 $167 3 $0 $0 4 $300 $166 CFs: PV of CFs: PV = $397.55 PV = $397.55 You can find the individual PVs and sum them. Alternately, you can automate the process using Excel or a calculator, by inputting the data into the cash flow register and pressing the NPV key. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 91. What is the present value of the following cash flow stream at a rate of 18.5%? Years: CFs: a. b. c. d. e. 0 $0 1 $1,500 2 $3,000 3 $4,500 4 $6,000 $10,247.31 $8,051.45 $7,228.01 $9,149.38 $8,325.94 ANS: D I/YR = 18.5% PV = PV = PV = 0 1 2 3 CFs: $0 $1,500 $3,000 $4,500 PV of CFs: $0 $1,266 $2,136 $2,704 $9,149.38 Found using the Excel NPV function $9,149.38 Found by summing individual PVs. $9,149.38 Found using the calculator NPV key. 4 $6,000 $3,043 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 92. What is the present value of the following cash flow stream at a rate of 10.0%? Years: 0 CFs: $750 1 $2,450 2 $3,175 3 $4,400 a. b. c. d. e. $8,907.02 $7,660.04 $10,866.57 $8,639.81 $7,303.76 ANS: A I/YR = 10.0% PV = PV = 0 1 2 3 CFs: $750 $2,450 $3,175 $4,400 PV of CFs: $750 $2,227 $2,624 $3,306 $8,907.02 Found by summing individual PVs. $8,907.02 Found with a calculator or Excel to automate the process. With a calculator, input the cash flows and into the cash flow register, then press the NPV key. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 93. You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 18.5%? 0 $0 CFs: a. b. c. d. e. 1 $1,000 2 $2,000 3 $2,000 4 $2,000 $3,363.26 $5,515.75 $4,484.35 $4,394.66 $4,708.57 ANS: C I/YR = 18.5% PV = PV = PV = 0 1 2 CFs: $0 $1,000 $2,000 PV of CFs: $0 $844 $1,424 Found using the Excel NPV function $4,484.35 $4,484.35 Found by summing individual PVs. $4,484.35 Found using the calculator NPV key. 3 $2,000 $1,202 4 $2,000 $1,014 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 94. At a rate of 5.0%, what is the future value of the following cash flow stream? Years: CFs: a. b. c. d. e. $552.35 $558.70 $514.26 $704.72 $634.88 0 $0 1 $75 2 $225 3 $0 4 $300 ANS: E I/YR = 5.0% FV = FV = FV = 0 1 2 3 4 CFs: $0 $75 $225 $0 $300 FV of CFs: $0 $87 $248 $0 $300 $634.88 Found by summing individual FVs. $634.88 Found with the NFV key in some calculators. $634.88 Found with a calculator by first finding the PV of the stream, then finding the FV of that PV. PV of the $522.32 stream: FV of the PV: $634.88 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 95. Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $13,500 at the end of the 5th year. What is the expected rate of return on this investment? a. 12.91% b. 10.46% c. 11.49% d. 15.23% e. 12.39% ANS: A CFs: 0 -$10,000 I/YR -$10,000 12.91% 1 $750 2 $750 3 $750 4 $750 5 $750 $13,500 $750 $750 $750 $750 $14,250 I is the discount rate that causes the PV of the inflows to equal the initial negative CF, and is found with Excel's IRR function or by inputting the CFs into a calculator and pressing the IRR key. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 96. You are offered a chance to buy an asset for $5,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset? a. 18.10% b. 19.96% c. 15.73% d. 16.91% e. 14.55% ANS: D CFs: I/YR 0 -$5,250 16.91% 1 2 3 4 $750 $1,000 $850 $6,250 I is the discount rate that causes the PV of the positive inflows to equal the initial negative CF. I can be found using Excel's IRR function or by inputting the CFs into a calculator and pressing the IRR key. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 97. What's the future value of $3,300 after 5 years if the appropriate interest rate is 6%, compounded semiannually? a. $5,100.16 b. $4,434.92 c. $4,390.57 d. $5,543.66 e. $5,233.21 ANS: B Years Periods/Yr Nom. I/YR 5 2 6.0% N = Periods PMT I = I/Period PV FV = 10 $0 3.0% $3,300 Could be found using a calculator, an equation, or Excel. $4,434.92 Note that we must first convert to periods and rate per period. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 98. What's the present value of $13,000 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually? a. $9,886.30 b. $10,198.50 c. $10,406.63 d. $10,718.83 e. $11,655.43 ANS: C Years Periods/Yr Nom. I/YR 5 2 4.5% FV N = Periods PMT I = I/Period PV = $13,000 10 $0 2.25% $10,406.63 Note that we must first convert to periods and rate per period. Could be found using a calculator, the equation, or Excel. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 99. What's the future value of $1,225 after 5 years if the appropriate interest rate is 6%, compounded monthly? a. $1,900.19 b. $1,652.34 c. $1,751.48 d. $1,371.44 e. $1,272.30 ANS: B Years Periods/Yr Nom. I/YR N = Periods PMT I/Period PV FV 5 12 6.0% 60 $0 0.5% $1,225 $1,652.34 Could be found using a calculator, the equation, or Excel. Note that we must first convert to periods and rate per period. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 100. What's the present value of $1,675 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly? a. $1,440.49 b. $1,241.80 c. $1,179.71 d. $1,266.63 e. $1,279.05 ANS: B Years Periods/Yr Nom. I/YR N=Periods PMT I/Period FV PV = PV = 5 12 6.0% 60 $0 0.5% $1,675 $1,241.80 = FV / (1+rPer)N $1,241.80 Found using a calculator or Excel PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 101. Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 23.50%, with interest paid monthly, what is the card's EFF%? a. 30.66% b. 26.20% c. 23.32% d. 22.80% e. 22.54% ANS: B APR = Nominal rate Periods/yr 23.50% 12 EFF% =(1+(rNOM/N))^N - 1 = 26.20% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 102. Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 6.3%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside? a. –0.38% b. –0.43% c. –0.40% d. –0.49% e. –0.30% ANS: C This problem can be worked using the interest conversion feature of a calculator or Excel. It could also be worked using the conversion formula. We used the conversion formula. Nominal rate, Riverside Nominal rate, Midwest Periods/yr, Riverside Periods/yr, Midwest EFF% Riverside EFF% Midwest Difference 6.5% 6.3% 12 1 = (1+(rNOM/N))^N - 1 = 6.70% 6.3% –0.40% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 103. Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 9.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan? a. 11.45% b. 7.26% c. 9.40% d. 9.31% e. 10.70% ANS: D Nominal I/YR 9.00% Periods/yr 4 EFF% = (1+(rNOM/N))^N - 1 = 9.31% You could also find the EFF% as follows: Interest paid each quarter = Loan rate/4 = Qtrly PMT = $225.00 Then find the IRR as a quarterly rate and convert to an annual rate. This procedure is obviously longer. CFs: 0 10,000.00 1 –225.00 2 –225.00 3 –225.00 4 –225.00 -10,000.00 10,000.00 –225.00 IRR (quarterly) = 2.25% Annual effective rate = 9.31% –225.00 –225.00 –10,225 vs. nominal rate = 9.00% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 104. Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $320.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan? a. 13.43% b. 15.71% c. 12.35% d. 12.62% e. 13.83% ANS: A Interest payment: 0 CFs: 10,000 10,000 IRR (quarterly) = Annual effective rate = $320.00 1 -320.00 -320.00 3.20% 13.43% 2 -320.00 3 -320.00 -320.00 -320.00 4 -320.00 -10,000 -10,320 vs. nominal rate 12.80% = PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 105. Charter Bank pays a 3.30% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay? a. 4.05% b. 3.52% c. 3.55% d. 3.35% e. 4.09% ANS: D Nominal I/YR 3.30% Periods/yr 12 Periodic rate 0.28% EFF% = (1+(rNOM/N))^N - 1 = 3.35% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 106. Suppose your credit card issuer states that it charges a 8.50% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate? a. 8.84% b. 7.69% c. 7.87% d. 11.05% e. 9.81% ANS: A Nominal I/YR = APR 8.50% Periods/yr 12 EFF% = (1+(rNOM/N))^N - 1 = 8.84% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 107. Pace Co. borrowed $12,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month? a. $89.18 b. $55.1 c. $72.50 d. $89.9 e. $75.4 ANS: C Nominal I/YR Days/yr Amount borrowed Interest per month 7.25% Days in month 360 Daily rate $12,000 Interest per day = Interest/day 30 = 30 0.020139% $2.41667 $72.50 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 108. Suppose you deposited $47,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days? a. $37,478.98 b. $40,886.16 c. $48,674.00 d. $55,488.36 e. $60,355.76 ANS: C Nominal I/YR Number of months Days in year Days in month Amount deposited Ending amount 5.25% Rate/day = rNOM/360 = 8 Days = Months 30 = 360 30 $47,000 $48,674.00 0.0146% 240 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 109. Suppose you borrowed $13,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be? a. $3,651.55 b. $4,012.69 c. $3,972.57 d. $4,373.83 e. $4,092.95 ANS: B Years = N I/YR FV Amount borrowed = PV Payments = PMT 4 9.0% $0 $13,000 $4,012.69 Found with a calculator, as the PMT. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 110. Suppose you are buying your first condo for $220,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be? a. $1,023.63 b. $1,580.80 c. $1,373.48 d. $1,049.55 e. $1,295.74 ANS: E Years Payments/year Nominal rate Purchase price Down payment 30 N 12 Periodic rate 6.50% PV $220,000 FV $15,000 PMT 360 0.54% $205,000 $0.00 $1,295.74 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 111. Your uncle will sell you his bicycle shop for $240,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be? a. $3,722.60 b. $4,712.16 c. $4,476.55 d. $3,675.48 e. $4,146.70 ANS: B Monthly annuity, so interest must be calculated on a monthly basis. Years 4 Payments/year 12 N 48 Nominal rate 6.0% PV 0.5% $240,000 I/period FV $50,000 PMT $4,712.16 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 112. Suppose you borrowed $15,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year? a. $1,680.00 b. $1,410.00 c. $1,500.00 d. $1,380.00 e. $1,710.00 ANS: C I/YR Years Amount borrowed Interest in Year 1 10.0% 5 $15,000 $1,500.00 Simply multiply the rate times the amount borrowed. PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 113. You plan to borrow $45,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2? a. $2,931.11 b. $3,110.56 c. $3,080.65 d. $2,990.92 e. $2,273.10 ANS: D Find the required payment: N 7 I 7.5% PV $45,000 FV $0 PMT $8,496.01 Found with a calculator or Excel. Amortization schedule (first 2 years) Year Beg. Balance Payment Interest 1 45,000.00 8,496.01 3,375.00 2 39,878.99 8,496.01 2,990.92 Principal 5,121.01 5,505.09 End. Balance 39,878.99 34,373.90 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 114. Your bank offers to lend you $180,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2? a. $14,269 b. $14,839 c. $14,982 d. $15,838 e. $10,987 ANS: A Find the required payment: N I PV FV PMT 10 8.5% $180,000 $0 $27,433 Found with a calculator or Excel. Amortization schedule (first 2 years) Year Payment Interest Principal 1 27,433 15,300 12,133 2 27,433 13,165 14,269 End. Balance 167,867 154,702 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 115. You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $360,000? Round fractional months up. a. 55 b. 49 c. 38 d. 55 e. 59 ANS: B BEGIN Mode I/YR I/MO PV PMT FV N 18.00% 1.50% Monthly annuity due, so interest must be calculated on monthly basis. rNOM / 12. $0 $5,000 $360,000 48.67 Rounded up: 49 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 116. You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $395,000? a. 89.16 b. 111.70 c. 110.72 d. 97.98 e. 81.32 ANS: D I/YR 7.00% I/MO 0.58% Monthly annuity, so interest must be calculated on monthly basis PV $0 PMT $3,000 FV $395,000 N $97.9784 PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 117. Your child's orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan? a. 17.81% b. 12.06% c. 14.36% d. 17.52% e. 15.08% ANS: C N PV PMT FV I/MO I/YR = I/MO 12 = 36 $4,000 $137.41 $0 1.20% Monthly annuity, so interest must be calculated on monthly basis 14.36% PTS: 1 DIF: MEDIUM NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 118. Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $930, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy? a. 20.72 b. 13.59 c. 16.57 d. 17.07 e. 16.91 ANS: C Find N for an annuity due with the indicated terms to determine how long you must live to make the lifetime subscription worthwhile. BEGIN Mode Interest rate (I/YR) Annual cost (PMT) Lifetime subscription cost (PV) Number of payments made (N) 6.0% $85 $930 16.57 PTS: 1 DIF: MEDIUM | HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 119. You just deposited $9,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now? a. b. c. d. e. $19,617.39 $19,378.16 $23,923.65 $18,421.21 $28,469.15 ANS: C Interest rate Periods/year Quarterly rate 1st deposit 2nd deposit 3rd deposit Years on Deposit 3 2 1 Quarters on Deposit 12 8 4 4.0% 4 1.0% $9,500 $5,000 $7,500 Ending Amount $10,704.84 $5,414.28 $7,804.53 $23,923.65 PTS: 1 DIF: MEDIUM | HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 120. Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 5.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks? a. –0.11% b. –0.07% c. –0.10% d. –0.08% e. –0.09% ANS: E Students must understand that "simple interest with interest paid quarterly" means that the bank gets the interest at the end of each quarter, hence it can invest it, presumably at the same nominal rate. This results in the same effective rate as if it were stated as "5%, quarterly compounding." Nominal rate, Farmers Periods/yr, Farmers Nominal rate, Merchants Periods/yr, Merchants EFF% Farmers EFF% Merchants Difference 5.0% 4 5.0% 1 5.09% 5.00% –0.09% PTS: 1 DIF: MEDIUM | HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 121. Suppose you borrowed $75,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year? a. b. c. d. e. $12,657.43 $15,695.21 $12,404.28 $13,037.15 $15,062.34 ANS: A Interest rate Years Amount borrowed Step 1: Find the PMT Step 2: Find the 1st year's interest Step 3: Subtract the interest from the payment; this is repayment of principal 8.5% 5 $75,000 19,032.43 6,375.00 12,657.43 PTS: 1 DIF: MEDIUM | HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 122. Suppose you borrowed $20,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment? a. $14,795.97 b. $13,133.50 c. $13,964.74 d. $16,624.68 e. $13,798.49 ANS: D Interest rate Years Amount borrowed Step 1: Find the PMT Step 2: Find the 1st year's interest Step 3: Subtract the interest from the payment; this is repayment of principal Step 4: Subtract the repayment of principal from the beginning amount owed 8.5% 5 $20,000 $5,075.32 $1,700.00 $3,375.32 $16,624.68 PTS: 1 DIF: MEDIUM | HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 123. Your sister turned 35 today, and she is planning to save $20,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year. a. $200,362.24 b. $155,837.30 c. $183,665.39 d. $185,520.60 e. $157,692.51 ANS: D Interest rate Years to retirement 7.5% 30 Years in retirement Amount saved per year Step 1: Find the amount at age 65; use the FV function Step 2: Find the PMT for a 25-year ordinary annuity using the FV you just found as the PV. 25 $20,000 2,067,988 185,520.60 PTS: 1 DIF: MEDIUM | HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 124. You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,200 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning? a. 10.14% b. 10.77% c. 7.79% d. 11.14% e. 9.05% ANS: E BEGIN Mode N 24 PV $0 PMT $500 FV $13,200 I/MO 0.75% I/YR 9.05% PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 125. Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 18.5% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal? a. 84.51% b. 80.29% c. 66.76% d. 91.27% e. 82.82% ANS: A N rNOM Per. r PV PMT FV 12 18.5% 1.5417% $72,500 $6,664 $0 % prin. = Prin2 / PMT = Amortization schedule(first 12 months) Month Beg. Balance Payment Interest 1 $72,500.00 $6,664 $664.58 2 $66,953.64 $6,664 $611.94 3 $61,321.78 $6,664 $558.81 84.51% Principal Ending Balance $5,546.36 $66,953.64 $5,631.86 $61,321.78 $5,718.69 $55,603.10 4 5 6 7 8 9 10 11 12 $55,603.10 $49,796.25 $43,899.88 $37,912.60 $31,833.03 $25,659.72 $19,391.24 $13,026.13 $6,562.89 $6,664 $6,664 $6,664 $6,664 $6,664 $6,664 $6,664 $6,664 $6,664 $505.20 $451.09 $396.49 $341.39 $285.78 $229.66 $173.03 $115.88 $58.20 $5,806.85 $5,896.37 $5,987.27 $6,079.58 $6,173.30 $6,268.48 $6,365.12 $6,463.24 $6,562.89 $49,796.25 $43,899.88 $37,912.60 $31,833.03 $25,659.72 $19,391.24 $13,026.13 $6,562.89 $0.00 PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 126. On January 1, 2009, your brother's business obtained a 30-year amortized mortgage loan for $425,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2009? a. $33,759.09 b. $34,055.22 c. $29,613.24 d. $29,317.10 e. $31,390.03 ANS: C Years Periods/yr N (12 mo.) PV = Loan FV 30 Nominal r 12 I/period 360 PMT $425,000 Interest, 2009 $0 7.00% 0.5833% $2,827.54 $29,613.24 Amortization schedule(first 3 months) Year Beg. Balance Payment Interest Principal End. Balance 1 425,000.00 2,827.54 2,479.17 348.37 424,651.63 2 424,651.63 2,827.54 2,477.13 350.40 424,301.23 3 424,301.23 2,827.54 2,475.09 352.45 423,948.78 4 423,948.78 2,827.54 2,473.03 354.50 423,594.28 5 423,594.28 2,827.54 2,470.97 356.57 423,237.71 6 423,237.71 2,827.54 2,468.89 358.65 422,879.07 7 422,879.07 2,827.54 2,466.79 360.74 422,518.32 8 422,518.32 2,827.54 2,464.69 362.85 422,155.48 9 422,155.48 2,827.54 2,462.57 364.96 421,790.52 10 421,790.52 2,827.54 2,460.44 367.09 421,423.43 11 421,423.43 2,827.54 2,458.30 369.23 421,054.19 12 421,054.19 2,827.54 2,456.15 371.39 420,682.81 33,930.43 29,613.24 4,317.19 PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 127. Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began putting $3,800 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $3,800 payments until a 46th and final payment is made on Steve's 65th birthday. The grandfather set things up this way because he wants Steve to work, not be a ""trust fund baby,"" but he also wants to ensure that Steve is provided for in his old age. Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed today, and he has instructed his trustee to make 40 additional equal annual payments until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday? a. $6,909 b. $5,889 c. $5,153 d. $5,663 e. $5,833 ANS: D Steve's retirement account Ed's retirement account No. of payments thus far, including 6 Payment today 1 today's payment Number of remaining payments 40 40 N = total payments 46 N 41 I/YR 8.0% I/YR 8.0% PV $0 PV $0 PMT $1,590,019 $3,800 FV = Ed's FV = FV Steve's FV = $1,590,019 PMT $5,663 PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 128. After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now? a. $330,578 b. $294,465 c. $277,797 d. $261,129 e. $255,573 ANS: C There are 3 cash flow streams: the gift and the two annuities. The gift will grow for 12 years. Then there is a 6-year annuity whose FV at the end of year 6 will compound for an additional 6 years. Finally, there is a second 6-year annuity. The sum of the compounded values of those three sets of cash flows is the final amount. Interest rate 1st annuity 9.0% $7,500 2nd annuity Gift Total years Annuity years Amount at end of Year 6 $56,425 NA NA $15,000 $25,000 12 6 Compound @ 9% Final amt: Amount at end of Year 12 $94,630 $112,850 $70,317 $277,797 PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 129. You are negotiating to make a 7-year loan of $27,500 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X? a. $5,683.99 b. $5,172.43 c. $5,513.47 d. $5,740.83 e. $5,058.75 ANS: A This is a relatively difficult problem for an efficient calculator solution or classroom exam, but it is appropriate for a challenging take-home or online. I/YR = 8% 0 1 -$27,500 $2,500 2 3 $5,000 $7,500 4 X 5 X 6 X 7 X Calculator solution: Step 1. Use the CF register to find the NPV of the 4 known cash flows, CF0 to -$14,944.75 CF3: Step 2. Find the FV of this NPV at the end of period 3, i.e., compound the NPV -$18,826.08 you found for 3 years. Step 3. Now find the PMT for a 4-year annuity with this PV. $5,683.99 PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 130. “John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). So far, John and Daphne have accumulated $13,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs?” a. $3,069.41 b. $3,598.62 c. $3,528.06 d. $4,374.80 e. $4,092.55 ANS: C Current college cost/year College cost inflation Return on investment account Payments at t = 1, 2, 3, and 4 Account balance at t = 0 $14,500 3.5% 9.0% $5,000 $13,000 1. Determine the cost of each year during college and its PV at t = 8, discounted at the return on investment. Cost PV at t-8 Year 1 (t = 8) = -19,093.73 -19,093.73 Current cost (1+infl)^8 = Year 2 (t = 9) = -19,762.01 -18,130.29 Prior year (1+infl) = Year 3 (t = 10) = -20,453.68 -17,215.45 Prior year (1+infl) = Year 4 (t = 11) = -21,169.56 -16,346.79 Prior year (1+infl) = Find PV (at t = 8) of all college costs = amount needed at t = 8: -70,786.26 2. Create a time line with those cash flows, plus the known initial CFs, as shown below. Put in for the unknownvalues for t = 5 - 7. We show the time line on two sets of rows. Ours now has the solution value, but it didn't originally. 0 1 2 3 4 5 Known values; X $13,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 X for unknown: Solution value for $2,412.76 X: Cash flows: $15,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $2,412.76 Cash flows, continued: 6 7 8 9 10 11 X X -$19,093.73 -$19,762.01 -$20,453.68 -$21,169.56 $2,412.76 $2,412.76 $2,412.76 $2,412.76 -$19,093.73 -$19,762.01 -$20,453.68 -$21,169.56 3. We found the PV of the college costs (t = 8-11) at t = 8 above. Their sum is shown to the right. 4. Find the FV of t = 0 & 4 positive CFs at t = 8 5. Find the difference between the positive and negative t = 8 values: 0 1 2 3 4 $15,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 -70,786.26 $25,903.31 $9,140.20 $8,385.50 $7,693.12 $7,057.91 $58,180.04 -$12,606.22 6. Find PMT for a 3-year annuity due whose FV is equal to this difference: PTS: 1 DIF: HARD NAT: Analytic skills LOC: Students will acquire an understanding of the time value of money. 3 $3,528.06