CHAPTER 1

CHAPTER 4TIME VALUE OF MONEY(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)

Please see the preface for information on the AACSB letter indicators (F, M, etc.) on the subject lines.

Multiple Choice: True/False

(4.2) CompoundingF JAnswer: a EASY[endnoteRef:1].Starting to invest early for retirement increases the benefits of compound interest. [1: .(4.2) CompoundingF JAnswer: a EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: b EASY[endnoteRef:2].Starting to invest early for retirement reduces the benefits of compound interest. [2: .(4.2) CompoundingF JAnswer: b EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: a EASY[endnoteRef:3].A time line is meaningful even if all cash flows do not occur annually. [3: .(4.2) CompoundingF JAnswer: a EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: b EASY[endnoteRef:4].A time line is not meaningful unless all cash flows occur annually. [4: .(4.2) CompoundingF JAnswer: b EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: a EASY[endnoteRef:5].Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly. [5: .(4.2) CompoundingF JAnswer: a EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: b EASY[endnoteRef:6].Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. [6: .(4.2) CompoundingF JAnswer: b EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: a EASY[endnoteRef:7].Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. [7: .(4.2) CompoundingF JAnswer: a EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: b EASY[endnoteRef:8].Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods. [8: .(4.2) CompoundingF JAnswer: b EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: a EASY[endnoteRef: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. [9: .(4.2) CompoundingF JAnswer: a EASY]

a.Trueb.False

(4.2) CompoundingF JAnswer: b EASY[endnoteRef: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. [10: .(4.2) CompoundingF JAnswer: b EASY]

a.Trueb.False

(4.3) PV versus FVC JAnswer: b EASY[endnoteRef: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. [11: .(4.3) PV versus FVC JAnswer: b EASY]

a.Trueb.False

(4.3) PV versus FVC JAnswer: a EASY[endnoteRef: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. [12: .(4.3) PV versus FVC JAnswer: a EASY]

a.Trueb.False

(4.3) PV versus FVC JAnswer: a EASY[endnoteRef:13].Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value. [13: .(4.3) PV versus FVC JAnswer: a EASY]

a.Trueb.False

(4.3) PV versus FVC JAnswer: b EASY[endnoteRef:14].Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value. [14: .(4.3) PV versus FVC JAnswer: b EASY]

a.Trueb.False

(4.15) Effective annual rateC JAnswer: b EASY[endnoteRef:15].If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate. [15: .(4.15) Effective annual rateC JAnswer: b EASY]

a.Trueb.False

(4.15) Effective annual rateC JAnswer: a EASY[endnoteRef:16].If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate. [16: .(4.15) Effective annual rateC JAnswer: a EASY]

a.Trueb.False

(4.18) Growing annuityC JAnswer: a EASY[endnoteRef:17].A growing annuity is a cash flow stream that grows at a constant rate for a specified number of periods. [17: .(4.18) Growing annuityC JAnswer: a EASY]

a.Trueb.False

(4.18) Growing annuityC JAnswer: b EASY[endnoteRef:18].A growing annuity is any cash flow stream that grows over time. [18: .(4.18) Growing annuityC JAnswer: b EASY]

a.Trueb.False

(4.2) CompoundingC JAnswer: b MEDIUM[endnoteRef:19].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. [19: .(4.2) CompoundingC JAnswer: b MEDIUM]

a.Trueb.False

(4.2) CompoundingC JAnswer: a MEDIUM[endnoteRef:20].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. [20: .(4.2) CompoundingC JAnswer: a MEDIUM]

a.Trueb.False

(4.2) Comparative compoundingC JAnswer: a MEDIUM[endnoteRef:21].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.) [21: .(4.2) Comparative compoundingC JAnswer: a MEDIUMWork out the numbers with a calculator:PV1000FVA =$1,710.34Rate on A5%2 FVA =$3,420.68Rate on B12%FVB =$3,478.55Years11FVB > 2 FVA, so TRUE]

a.Trueb.False

(4.2) Comparative compoundingC JAnswer: b MEDIUM[endnoteRef:22].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.) [22: .(4.2) Comparative compoundingC JAnswer: b MEDIUMWork out the numbers with a calculator:PV1000FVA =$1,710.34Rate on A5%2 FVA =$3,420.68Rate on B12%FVB =$3,478.55Years11FVB > 2 FVA, so FALSE]

a.Trueb.False

(4.3) PV of a dollarC JAnswer: a MEDIUM[endnoteRef:23].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. [23: .(4.3) PV of a dollarC JAnswer: a MEDIUM]

a.Trueb.False

(4.3) PV of a sumC JAnswer: b MEDIUM[endnoteRef:24].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. [24: .(4.3) PV of a sumC JAnswer: b MEDIUM]

a.Trueb.False

(4.9) PV of an annuityC JAnswer: a MEDIUM[endnoteRef:25].All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases. [25: .(4.9) PV of an annuityC JAnswer: a MEDIUMOne 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.]

a.Trueb.False

(4.9) PV of an annuityC JAnswer: b MEDIUM[endnoteRef:26].All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases. [26: .(4.9) PV of an annuityC JAnswer: b MEDIUMOne 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.]

a.Trueb.False

(4.15) Periodic and nominal ratesC JAnswer: a MEDIUM[endnoteRef:27].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. [27: .(4.15) Periodic and nominal ratesC JAnswer: a MEDIUM]

a.Trueb.False

(4.15) Periodic and nominal ratesC JAnswer: b MEDIUM[endnoteRef:28].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. [28: .(4.15) Periodic and nominal ratesC JAnswer: b MEDIUM]

a.Trueb.False

(4.15) Effective and nominal ratesC JAnswer: a MEDIUM[endnoteRef:29].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). [29: .(4.15) Effective and nominal ratesC JAnswer: a MEDIUM]

a.Trueb.False

(4.15) Effective and nominal ratesC JAnswer: b MEDIUM[endnoteRef:30].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). [30: .(4.15) Effective and nominal ratesC JAnswer: b MEDIUM]

a.Trueb.False

(4.17) AmortizationC JAnswer: b MEDIUM[endnoteRef:31].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. [31: .(4.17) AmortizationC JAnswer: b MEDIUM]

a.Trueb.False

(4.17) AmortizationC JAnswer: a MEDIUM[endnoteRef:32].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. [32: .(4.17) AmortizationC JAnswer: a MEDIUM]

a.Trueb.False

(4.17) AmortizationC JAnswer: a MEDIUM[endnoteRef:33].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. [33: .(4.17) AmortizationC JAnswer: a MEDIUM]

a.Trueb.False

(4.17) AmortizationC JAnswer: b MEDIUM[endnoteRef:34].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. [34: .(4.17) AmortizationC JAnswer: b MEDIUM]

a.Trueb.False

(4.17) AmortizationC JAnswer: b HARD[endnoteRef:35].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. [35: .(4.17) AmortizationC JAnswer: b HARDThere is no reason to think that this statement would always be true. The portion of the payment 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 3year 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$1,000Original loan$1,000Rate10%Rate41.45%Life3Life3Payment$402.11Payment$640.98Beg. BalanceInterestPrincipalEnd. Bal.Beg. BalanceInterestPrincipalEnd. Bal.1$1,000.00$100.00$302.11$697.891$1,000.00$414.50$226.48$773.522$697.89$69.79$332.33$365.562$773.52$320.62$320.36$453.153$365.56$36.56$365.56$0.003$453.15$187.83$453.15$0.00]

a.Trueb.False

(4.17) AmortizationC JAnswer: a HARD[endnoteRef:36].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. [36: .(4.17) AmortizationC JAnswer: a HARDThis 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$1,000Original loan$1,000Rate10%Rate41.45%Life3Life3Payment$402.11Payment$640.98Beg. BalanceInterestPrincipalEnd. Bal.Beg. BalanceInterestPrincipalEnd. Bal.1$1,000.00$100.00$302.11$697.891$1,000.00$414.50$226.48$773.522$697.89$69.79$332.33$365.562$773.52$320.62$320.36$453.153$365.56$36.56$365.56$0.003$453.15$187.83$453.15$0.00]

a.Trueb.False

Multiple Choice: Conceptual

The correct answers to most of these questions can be determined without doing any calculations. However, calculations are required for a few of them, and calculations are useful to confirm the answers to several others. You can see from the answer where calculations are required. Those questions generally take students longer to answer.

(4.1) Time linesF JAnswer: b MEDIUM[endnoteRef:37].Which of the following statements is CORRECT? [37: .(4.1) Time linesF JAnswer: b MEDIUM]

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.

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Page 10True/FalseChapter 4: Time Value of Money 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.Chapter 4: Time Value of MoneyTrue/FalsePage 9

(4.1) Time linesF JAnswer: d MEDIUM[endnoteRef:38].Which of the following statements is CORRECT? [38: .(4.1) Time linesF JAnswer: d MEDIUM]

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.

(4.1) Time linesF JAnswer: c MEDIUM[endnoteRef:39].Which of the following statements is CORRECT? [39: .(4.1) Time linesF JAnswer: c MEDIUM]

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.

(4.1) Time linesF JAnswer: e MEDIUM[endnoteRef:40].Which of the following statements is CORRECT? [40: .(4.1) Time linesF JAnswer: e MEDIUM]

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.

(4.3) Effects of factors on PVsC JAnswer: b MEDIUM[endnoteRef:41].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? [41: .(4.3) Effects of factors on PVsC JAnswer: b MEDIUM]

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 investments 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.

(4.3) Effects of factors on PVsC JAnswer: b MEDIUM[endnoteRef:42].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? [42: .(4.3) Effects of factors on PVsC JAnswer: b MEDIUM]

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 investments 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.

(4.6) AnnuitiesF JAnswer: d MEDIUM[endnoteRef:43].Which of the following statements is CORRECT? [43: .(4.6) AnnuitiesF JAnswer: d MEDIUM]

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.

(4.6) AnnuitiesF JAnswer: c MEDIUM[endnoteRef:44].Which of the following statements is CORRECT? [44: .(4.6) AnnuitiesF JAnswer: c MEDIUM]

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.

(4.15) Quarterly compoundingC JAnswer: c MEDIUM[endnoteRef:45].Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? [45: .(4.15) Quarterly compoundingC JAnswer: c MEDIUM]

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%.

(4.15) Quarterly compoundingC JAnswer: d MEDIUM[endnoteRef:46].Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? [46: .(4.15) Quarterly compoundingC JAnswer: d MEDIUM]

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%.

(4.17) AmortizationC JAnswer: c MEDIUM[endnoteRef:47].A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? [47: .(4.17) AmortizationC JAnswer: c MEDIUMa, d, and e can be ruled out as incorrect by simple reasoning. b is also incorrect because interest in the first year would be Loan amount interest rate regardless of the life of the loan, so the interest payment would be identical for the first payment. Think about the situation where r = 0%, statement c is the "most logical guess." One could also set up an amortization schedule and change the numbers to confirm that only c 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.

(4.17) AmortizationC JAnswer: d MEDIUM[endnoteRef:48].A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? [48: .(4.17) AmortizationC JAnswer: d MEDIUMa, c, and e are obviously incorrect. b is also incorrect because interest in the first year would be Loan amount interest rate regardless of the life of the loan. That makes d the "most logical guess." One could also set up an amortization schedule and change the numbers to confirm that only d 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.

(4.17) AmortizationC JAnswer: b MEDIUM[endnoteRef:49].Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) [49: .(4.17) AmortizationC JAnswer: b MEDIUMb is the correct answer. Thinking through the question, the other answers can all be eliminated. One could also set up an amortization schedule to prove that only statement b is correct.]

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 loans life.

(4.17) AmortizationC JAnswer: e MEDIUM[endnoteRef:50].Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) [50: .(4.17) AmortizationC JAnswer: e MEDIUMe is the correct answer. Thinking through the question, the other answers can all be eliminated. One could also set up an amortization schedule to prove that only statement e is correct.]

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 loans life.

(4.17) AmortizationC JAnswer: b MEDIUM[endnoteRef:51].Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? [51: .(4.17) AmortizationC JAnswer: b MEDIUMb is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we could set up an example to see:Loan100000Term30Rate10%Periods/Year12Periodic rate0.008333333Total periods360Payment-$877.57Interest, Month 1$833.33Interest as % of total #360 payment:1%Interest, Month 360$7.25Principal as % of total #360 payment99%Principal, Month 360$870.32]

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.

(4.17) AmortizationC JAnswer: b MEDIUM[endnoteRef:52].Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? [52: .(4.17) AmortizationC JAnswer: b MEDIUMb is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we could set up an example to see:Loan100000Term30Rate10%Periods/Year12Periodic rate0.00833333Total periods360Payment-$877.57Interest Month 1$833.33Interest as % of total payment:95%, which is much larger than 10%.]

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.

(Comp.) Time value conceptsC JAnswer: a MEDIUM[endnoteRef:53].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. [53: .(Comp.) Time value conceptsC JAnswer: a MEDIUMA 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$4,382.79LargestEFF%10.00%10250B$4,081.59NOM%9.76%125C$4,280.81125D$2,500.002500E$3,984.36250]

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).

(Comp.) Time value conceptsC JAnswer: d MEDIUM[endnoteRef:54].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. [54: .(Comp.) Time value conceptsC JAnswer: d MEDIUMA 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$1,536.14EFF%10.00%10250B$1,573.63NOM%9.76%125C$1,650.44125D$963.86Smallest2500E$1,689.76250]

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).

(Comp.) Time value conceptsC JAnswer: d MEDIUM[endnoteRef:55].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? [55: .(Comp.) Time value conceptsC JAnswer: d MEDIUM]

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.

(Comp.) Time value conceptsC JAnswer: e MEDIUM[endnoteRef:56].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? [56: .(Comp.) Time value conceptsC JAnswer: e MEDIUM]

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.

(Comp.) Time value conceptsC JAnswer: c MEDIUM[endnoteRef:57].Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant? [57: .(Comp.) Time value conceptsC JAnswer: c MEDIUM]

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.

(Comp.) Time value conceptsC JAnswer: d MEDIUM[endnoteRef:58].Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant? [58: .(Comp.) Time value conceptsC JAnswer: d MEDIUM]

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.

(Comp.) Time value conceptsC JAnswer: a MEDIUM[endnoteRef:59].Which of the following statements is CORRECT? [59: .(Comp.) Time value conceptsC JAnswer: a MEDIUM]

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%.

(Comp.) Time value conceptsC JAnswer: b MEDIUM[endnoteRef:60].Which of the following statements is CORRECT? [60: .(Comp.) Time value conceptsC JAnswer: b MEDIUM]

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%.

(Comp.) AnnuitiesC JAnswer: d MEDIUM[endnoteRef:61].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? [61: .(Comp.) AnnuitiesC JAnswer: d MEDIUM]

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.

(Comp.) AnnuitiesC JAnswer: a MEDIUM[endnoteRef:62].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? [62: .(Comp.) AnnuitiesC JAnswer: a MEDIUM]

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.

(4.14) Solving for I: uneven CFsC JAnswer: c HARD[endnoteRef:63].Which of the following statements is CORRECT? [63: .(4.14) Solving for I: uneven CFsC JAnswer: c HARD]

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.

(4.14) Solving for I: uneven CFsC JAnswer: e HARD[endnoteRef:64].Which of the following statements is CORRECT? [64: .(4.14) Solving for I: uneven CFsC JAnswer: e HARD]

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.

(4.15) Effective annual rateC JAnswer: e HARD[endnoteRef:65].Which of the following bank accounts has the highest effective annual return? [65: .(4.15) Effective annual rateC JAnswer: e HARDBy inspection, we can see that e dominates a and b, and that c dominates d because, with the same interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be either e or c. Moreover, we can see by inspection that since c and e have the same compounding frequency yet e has the higher nominal rate, e must have the higher EFF%. You could also prove that e is the correct choice by calculating the EFF%s:a.8.300% = (1+0.08/12)12-1b.8.000% = (1+0.08/1)1-1c.7.250% = (1+0.07/365)365-1d.7.229% = (1+0.07/12)12-1e.8.328% = (1+0.08/365)365-1]

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.

2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Page 20Conceptual M/CChapter 4: Time Value of Money 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chapter 4: Time Value of MoneyConceptual M/CPage 19(4.15) Effective annual rateC JAnswer: d HARD[endnoteRef:66].Which of the following bank accounts has the lowest effective annual return? [66: .(4.15) Effective annual rateC JAnswer: d HARDBy inspection, we can see that b must have a lower EFF% than either a or e because they all pay the same nominal rate but b is compounded least frequently. Similarly, c and d pay the same rate, but d is compounded less frequently, hence d must have the lower EFF%. So, the correct answer must be either b or d. It is not obvious which of these two has the lower EFF%, so we must do a quick calculation to determine the correct response. As the following calculations show, d is the correct answer.a.8.300% = (1+0.08/12)12-1b.8.000% = (1+0.08/1)1-1c.7.250% = (1+0.07/365)365-1d.7.229% = (1+0.07/12)12-1e.8.328% = (1+0.08/365)365-1]

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.

(4.15) Effective annual rateC JAnswer: e HARD[endnoteRef:67].You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest? [67: .(4.15) Effective annual rateC JAnswer: e HARDBy inspection, we can see that e dominates b, c, and d because, with the same interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be either a or e. However, we cannot tell by inspection whether a or e provides the higher EFF%. We know that with one compounding period an EFF% is 6.1%, so we can calculate e's EFF%. It is 6.183%, so e is the correct answer.a. = (1+0.061/12)12-1 = 6.100%e. = (1+0.06/365)365-1 = 6.183%]

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.

Multiple Choice: Problems

(4.2) FV of a lump sumC JAnswer: d EASY[endnoteRef:68].Ellen now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding? [68: .(4.2) FV of a lump sumC JAnswer: d EASYN8I/YR8.5%PV$125PMT$0FV$240.08]

a.$205.83b.$216.67c.$228.07d.$240.08e.$252.08

(4.2) FV of a lump sumC JAnswer: d EASY[endnoteRef:69].Jose now has $500. How much would he have after 6 years if he leaves it invested at 5.5% with annual compounding? [69: .(4.2) FV of a lump sumC JAnswer: d EASYN6I/YR5.5%PV$500PMT$0FV$689.42]

a.$591.09b.$622.20c.$654.95d.$689.42e.$723.89

(4.2) FV of a lump sumC JAnswer: a EASY[endnoteRef:70].Suppose you have $1,500 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? [70: .(4.2) FV of a lump sumC JAnswer: a EASYN5I/YR3.5%PV$1,500PMT$0FV$1,781.53]

a.$1,781.53b.$1,870.61c.$1,964.14d.$2,062.34e.$2,165.46(4.2) FV of a lump sumC JAnswer: a EASY[endnoteRef:71].Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures? [71: .(4.2) FV of a lump sumC JAnswer: a EASYN10I/YR6.5%PV$2,000PMT$0FV$3,754.27]

a.$3,754.27b.$3,941.99c.$4,139.09d.$4,346.04e.$4,563.34

(4.2) FV of a lump sumC JAnswer: c EASY[endnoteRef:72].Last year Rocco Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later? [72: .(4.2) FV of a lump sumC JAnswer: c EASYN5I/YR6.0%PV$225.00PMT$0.00FV$301.10]

a.$271.74b.$286.05c.$301.10d.$316.16e.$331.96

(4.2) FV of a lump sumC JAnswer: c EASY[endnoteRef:73].Last year Tempe Corporation's sales were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later? [73: .(4.2) FV of a lump sumC JAnswer: c EASYN8I/YR7.5%PV$525.00PMT$0.00FV$936.33]

a.$845.03b.$889.51c.$936.33d.$983.14e.$1,032.30

(4.2) FV of a lump sumC JAnswer: b EASY[endnoteRef:74].How much would $1, growing at 3.5% per year, be worth after 75 years? [74: .(4.2) FV of a lump sumC JAnswer: b EASYN75I/YR3.5%PV$1.00PMT$0.00FV$13.20]

a.$12.54b.$13.20c.$13.86d.$14.55e.$15.28

(4.2) FV of a lump sumC JAnswer: b EASY[endnoteRef:75].How much would $100, growing at 5% per year, be worth after 75 years? [75: .(4.2) FV of a lump sumC JAnswer: b EASYN75I/YR5.0%PV$100.00PMT$0.00FV$3,883.27]

a.$3,689.11b.$3,883.27c.$4,077.43d.$4,281.30e.$4,495.37

(4.2) FV of a lump sumC JAnswer: b EASY[endnoteRef:76].You deposit $1,000 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? [76: .(4.2) FV of a lump sumC JAnswer: b EASYN25I/YR3.5%PV$1,000PMT$0FV$2,363.24]

a.$2,245.08b.$2,363.24c.$2,481.41d.$2,605.48e.$2,735.75

(4.2) FV of a lump sumC JAnswer: b EASY[endnoteRef:77].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 25 years? [77: .(4.2) FV of a lump sumC JAnswer: b EASYN25I/YR3.5%PV$500PMT$0FV$1,181.62]

a.$1,122.54b.$1,181.62c.$1,240.70d.$1,302.74e.$1,367.88

(4.3) PV of a lump sumC JAnswer: a EASY[endnoteRef:78].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 5.5%, how much is the bond worth today? [78: .(4.3) PV of a lump sumC JAnswer: a EASYN10I/YR5.5%PMT$0FV$1,000.00PV$585.43]

a.$585.43b.$614.70c.$645.44d.$677.71e.$711.59

(4.3) PV of a lump sumC JAnswer: a EASY[endnoteRef:79].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 5.5%, how much is the bond worth today? [79: .(4.3) PV of a lump sumC JAnswer: a EASYN8I/YR5.5%PMT$0FV$1,000.00PV$651.60]

a.$651.60b.$684.18c.$718.39d.$754.31e.$792.02

(4.3) PV of a lump sumC JAnswer: e EASY[endnoteRef:80].How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%? [80: .(4.3) PV of a lump sumC JAnswer: e EASYN50I/YR7.5%PMT$0FV$20,000PV$537.78]

a.$438.03b.$461.08c.$485.35d.$510.89e.$537.78

(4.3) PV of a lump sumC JAnswer: e EASY[endnoteRef:81].How much would $5,000 due in 25 years be worth today if the discount rate were 5.5%? [81: .(4.3) PV of a lump sumC JAnswer: e EASYN25I/YR5.5%PMT$0FV$5,000PV$1,311.17]

a.$1,067.95b.$1,124.16c.$1,183.33d.$1,245.61e.$1,311.17

(4.3) PV of a lump sumC JAnswer: b EASY[endnoteRef:82].Suppose a U.S. treasury bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today? [82: .(4.3) PV of a lump sumC JAnswer: b EASYN5I/YR4.25%PMT$0FV$2,500.00PV$2,030.30]

a.$1,928.78b.$2,030.30c.$2,131.81d.$2,238.40e.$2,350.32

(4.3) PV of a lump sumC JAnswer: b EASY[endnoteRef:83].Suppose an ExxonMobil Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4.25%, how much is the bond worth today? [83: .(4.3) PV of a lump sumC JAnswer: b EASYN10I/YR4.25%PMT$0FV$4,500.00PV$2,967.92]

a.$2,819.52b.$2,967.92c.$3,116.31d.$3,272.13e.$3,435.74

(4.4) Finding IC JAnswer: d EASY[endnoteRef:84].Suppose the U.S. Treasury offers to sell you a bond for $747.25. 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? [84: .(4.4) Finding IC JAnswer: d EASYN5PV$747.25PMT$0FV$1,000.00I/YR6.00%]

a.4.37%b.4.86%c.5.40%d.6.00%e.6.60%

(4.4) Finding IC JAnswer: d EASY[endnoteRef:85].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 $5,000. What interest rate would you earn if you bought this bond at the offer price? [85: .(4.4) Finding IC JAnswer: d EASYN10PV$3,000.00PMT$0FV$5,000.00I/YR5.24%]

a.3.82%b.4.25%c.4.72%d.5.24%e.5.77%

(4.4) Growth rateC JAnswer: b EASY[endnoteRef:86].Ten years ago, Spielberg Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in earnings per share (EPS) over the 10-year period? [86: .(4.4) Growth rateC JAnswer: b EASYN10PV$0.50PMT$0FV$2.20I/YR15.97%]

a.15.17%b.15.97%c.16.77%d.17.61%e.18.49%

(4.4) Growth rateC JAnswer: b EASY[endnoteRef:87].Five years ago, Greenery Inc. earned $1.50 per share. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period? [87: .(4.4) Growth rateC JAnswer: b EASYN5PV$1.50PMT$0FV$3.20I/YR16.36%]

a.15.54%b.16.36%c.17.18%d.18.04%e.18.94%(4.5) Finding NC JAnswer: e EASY[endnoteRef:88].Wendy has $5,000 invested in a bank that pays 3.8% annually. How long will it take for her funds to triple? [88: .(4.5) Finding NC JAnswer: e EASYI/YR3.8%PV$5,000.00PMT$0FV$15,000.00N29.46]

a.23.99b.25.26c.26.58d.27.98e.29.46

(4.5) Finding NC JAnswer: e EASY[endnoteRef:89].Chuck has $2,500 invested in a bank that pays 4% annually. How long will it take for his funds to double? [89: .(4.5) Finding NC JAnswer: e EASYI/YR4.0%PV$2,500.00PMT$0FV$5,000.00N17.67]

a.14.39b.15.15c.15.95d.16.79e.17.67

(4.5) Finding NC JAnswer: d EASY[endnoteRef:90].Last year Ellis Inc's earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Ellis EPS to triple? [90: .(4.5) Finding NC JAnswer: d EASYI/YR9.0%PV$3.50PMT$0FV$10.50N12.75]

a.9.29b.10.33c.11.47d.12.75e.14.02

(4.5) Finding NC JAnswer: e EASY[endnoteRef:91].You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20? [91: .(4.5) Finding NC JAnswer: e EASYI/YR8.0%PV$5,000.00PMT$0FV$9,140.20N7.84]

a.5.14b.5.71c.6.35d.7.05e.7.84

(4.5) Finding NC JAnswer: e EASY[endnoteRef:92].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 $30,000? [92: .(4.5) Finding NC JAnswer: e EASYI/YR6.0%PV$10,000.00PMT$0FV$30,000.00N18.85]

a.12.37b.13.74c.15.27d.16.97e.18.85

(4.7) FV of ordinary annuityC JAnswer: c EASY[endnoteRef:93].You want to buy a new sports car 3 years from now, and you plan to save $4,200 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? [93: .(4.7) FV of ordinary annuityC JAnswer: c EASYN3I/YR5.2%PV$0.00PMT$4,200FV$13,266.56]

a.$11,973b.$12,603c.$13,267d.$13,930e.$14,626

(4.7) FV of ordinary annuityC JAnswer: c EASY[endnoteRef:94].You want to buy a new ski boat 2 years from now, and you plan to save $8,200 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? [94: .(4.7) FV of ordinary annuityC JAnswer: c EASYN2I/YR6.2%PV$0.00PMT$8,200FV$16,908]

a.$15,260b.$16,063c.$16,908d.$17,754e.$18,642

(4.7) FV of ordinary annuityC JAnswer: a EASY[endnoteRef:95].You want to go to Europe 5 years from now, and you can save $3,100 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? [95: .(4.7) FV of ordinary annuityC JAnswer: a EASYN5I/YR8.5%PV$0.00PMT$3,100FV$18,369]

a.$18,369b.$19,287c.$20,251d.$21,264e.$22,327

(4.8) FV of annuity dueC JAnswer: a EASY[endnoteRef:96].You want to quit your job and go back to school for a law degree 4 years from now, and you plan to save $3,500 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? [96: .(4.8) FV of annuity dueC JAnswer: a EASYBEGIN ModeN4Alternative setup:I/YR5.7%01234PV$0.00$3,500$3,500$3,500$3,500PMT$3,500FV = $16,112FV$16,112]

a.$16,112b.$16,918c.$17,763d.$18,652e.$19,584

(4.8) FV of annuity dueC JAnswer: c EASY[endnoteRef:97].You want to quit your job and return to school for an MBA degree 3 years from now, and you plan to save $7,000 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? [97: .(4.8) FV of annuity dueC JAnswer: c EASYBEGIN ModeN3Alternative setup:I/YR5.2%0123PV$0.00$7,000$7,000$7,000$7,000PMT$7,000 FV = $23,261FV$23,261]

a.$20,993b.$22,098c.$23,261d.$24,424e.$25,645

(4.9) PV of ordinary annuityC JAnswer: e EASY[endnoteRef:98].What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%? [98: .(4.9) PV of ordinary annuityC JAnswer: e EASYN10I/YR5.5%PMT$2,700FV$0.00PV$20,352]

a.$16,576b.$17,449c.$18,367d.$19,334e.$20,352

(4.9) PV of ordinary annuityC JAnswer: e EASY[endnoteRef:99].What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%? [99: .(4.9) PV of ordinary annuityC JAnswer: e EASYN5I/YR4.5%PMT$4,700FV$0.00PV$20,633]

a.$16,806b.$17,690c.$18,621d.$19,601e.$20,633(4.9) PV of ordinary annuityC JAnswer: e EASY[endnoteRef:100].You have a chance to buy an annuity that pays $2,500 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? [100: .(4.9) PV of ordinary annuityC JAnswer: e EASYN3I/YR5.5%PMT$2,500FV$0.00PV$6,744.83]

a.$5,493.71b.$5,782.85c.$6,087.21d.$6,407.59e.$6,744.83

(4.9) PV of ordinary annuityC JAnswer: e EASY[endnoteRef:101].You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 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? [101: .(4.9) PV of ordinary annuityC JAnswer: e EASYN20I/YR5.0%PMT$5,000FV$0.00PV$62,311]

a.$50,753b.$53,424c.$56,236d.$59,195e.$62,311

(4.9) PV of ordinary annuityC JAnswer: b EASY[endnoteRef:102].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 $50,000 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? [102: .(4.9) PV of ordinary annuityC JAnswer: b EASYN30I/YR7.25%PMT$50,000FV$0.00PV$605,183]

a.$574,924b.$605,183c.$635,442d.$667,214e.$700,575

(4.9) PV of annuity dueC JAnswer: a EASY[endnoteRef:103].What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%? [103: .(4.9) PV of annuity dueC JAnswer: a EASYBEGIN ModeN5I/YR5.5%PMT$2,500FV$0.00PV$11,262.88]

a.$11,262.88b.$11,826.02c.$12,417.32d.$13,038.19e.$13,690.10

(4.11) PV of a perpetuityC JAnswer: b EASY[endnoteRef:104].Whats the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%? [104: .(4.11) PV of a perpetuityC JAnswer: b EASYI/YR5.0%PMT$250PV$5,000]

a.$4,750b.$5,000c.$5,250d.$5,513e.$5,788(4.11) Return on a perpetuityC JAnswer: a EASY[endnoteRef:105].Whats the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year? [105: .(4.11) Return on a perpetuityC JAnswer: a EASYCost (PV)$950PMT$85I/YR8.95%]

a.8.95%b.9.39%c.9.86%d.10.36%e.10.88%

(4.9) PV of annuity dueC JAnswer: c MEDIUM[endnoteRef:106].You have a chance to buy an annuity that pays $550 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? [106: .(4.9) PV of annuity dueC JAnswer: c MEDIUMBEGIN ModeN3I/YR5.5%PMT$550FV$0.00PV$1,565.48]

a.$1,412.84b.$1,487.20c.$1,565.48d.$1,643.75e.$1,725.94

(4.9) PV of annuity dueC JAnswer: c MEDIUM[endnoteRef:107].You have a chance to buy an annuity that pays $5,000 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? [107: .(4.9) PV of annuity dueC JAnswer: c MEDIUMBEGIN ModeN5I/YR4.5%PMT$5,000FV$0.00PV$22,938]

a20,701b.$21,791c.$22,938d.$24,085e.$25,289

(4.9) PV of annuity dueC JAnswer: d MEDIUM[endnoteRef:108].Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 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? [108: .(4.9) PV of annuity dueC JAnswer: d MEDIUMBEGIN ModeN20I/YR5.25%PMT$75,000FV$0.00PV$963,213]

a.$825,835b.$869,300c.$915,052d.$963,213e.$1,011,374

(4.9) PV of annuity dueC JAnswer: d MEDIUM[endnoteRef:109].Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 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? [109: .(4.9) PV of annuity dueC JAnswer: d MEDIUMBEGIN ModeN25I/YR5.15%PMT$85,000FV$0.00PV$1,240,960]

a.$1,063,968b.$1,119,966c.$1,178,912d.$1,240,960e.$1,303,008

(4.9) PV of annuity dueC JAnswer: b MEDIUM[endnoteRef:110].You inherited an oil well that will pay you $25,000 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? [110: .(4.9) PV of annuity dueC JAnswer: b MEDIUMBEGIN ModeN25I/YR7.5%PMT$25,000FV$0.00PV$299,574]

a.$284,595b.$299,574c.$314,553d.$330,281e.$346,795

(4.9) PV of annuity dueC JAnswer: b MEDIUM[endnoteRef:111].Sam was injured in an accident, and the insurance company has offered him the choice of $25,000 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? [111: .(4.9) PV of annuity dueC JAnswer: b MEDIUMBEGIN ModeN15I/YR7.5%PMT$25,000FV$0.00PV$237,229]

a.$225,367b.$237,229c.$249,090d.$261,545e.$274,622

(4.9) PV of ord. ann. & end. pmt.C JAnswer: e MEDIUM[endnoteRef:112].Whats the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%? [112: .(4.9) PV of ord. ann. & end. pmt.C JAnswer: e MEDIUMAlternative setup:N401234I/YR5.0%$2,250$2,250$2,250$2,250PMT$2,250$3,000FV$3,000$2,250$2,250$2,250$5,250PV$10,446PV = $10,446.50]

a.$8,509b.$8,957c.$9,428d.$9,924e.$10,446

(4.10) Payments on ord. annuityC JAnswer: a MEDIUM[endnoteRef:113].Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years? [113: .(4.10) Payments on ord. annuityC JAnswer: a MEDIUMN20I/YR8.25%PV$275,000FV$0.00PMT$28,532]

a.$28,532b.$29,959c.$31,457d.$33,030e.$34,681

(4.10) Payments on ord. annuityC JAnswer: d MEDIUM[endnoteRef:114].Your uncle has $375,000 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? [114: .(4.10) Payments on ord. annuityC JAnswer: d MEDIUMN25I/YR7.5%PV$375,000FV$0.00PMT$33,641.50]

a.$28,843.38b.$30,361.46c.$31,959.43d.$33,641.50e.$35,323.58

(4.10) Payments on annuity dueC JAnswer: c MEDIUM[endnoteRef:115].Your uncle has $375,000 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? [115: .(4.10) Payments on annuity dueC JAnswer: c MEDIUMBEGIN ModeN25I/YR7.5%PV$375,000FV$0.00PMT$31,294.42]

a.$28,243.21b.$29,729.70c.$31,294.42d.$32,859.14e.$34,502.10

(4.10) Payments on annuity dueC JAnswer: c MEDIUM[endnoteRef:116].Your grandmother just died and left you $100,000 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? [116: .(4.10) Payments on annuity dueC JAnswer: c MEDIUMBEGIN ModeN4I/YR6.5%PV$100,000FV$0.00PMT$27,409]

a.$24,736b.$26,038c.$27,409d.$28,779e.$30,218

(4.10) Payments on annuity dueC JAnswer: d MEDIUM[endnoteRef:117].Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years? [117: .(4.10) Payments on annuity dueC JAnswer: d MEDIUMBEGIN ModeN20I/YR8.25%PV$275,000FV$0.00PMT$26,357.92]

a.$22,598.63b.$23,788.03c.$25,040.03d.$26,357.92e.$27,675.82(4.10) Years to deplete ord. ann.C JAnswer: a MEDIUM[endnoteRef:118].Your father's employer was just acquired, and he was given a severance payment of $375,000, 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. What is the maximum number of whole payments that can be withdrawn before the account is exhausted; i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.) [118: .(4.10) Years to deplete ord. ann.C JAnswer: a MEDIUMI/YR7.5%PV$375,000PMT$35,000FV$0.00N22.50N rounded22]

a.22b.23c.24d.25e.26

(4.10) Years to deplete ord. ann.C JAnswer: b MEDIUM[endnoteRef:119].Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning 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. What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.) [119: .(4.10) Years to deplete ord. ann.C JAnswer: b MEDIUMI/YR7.50%PV$300,000PMT$35,000FV$25,000N13.48N rounded13]

a.12b.13c.14d.15e.16

(4.10) Years to deplete ann. dueC JAnswer: e MEDIUM[endnoteRef:120].Your Aunt Elsa has $500,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. What is the maximum number of whole payments that can be withdrawn before the account is exhausted; i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.) [120: .(4.10) Years to deplete ann. dueC JAnswer: e MEDIUMBEGIN ModeI/YR6.5%PV$500,000PMT$40,000FV$0.00N22.86N rounded22]

a.18b.19c.20d.21e.22

(4.10) Years to deplete ann. dueC JAnswer: c MEDIUM[endnoteRef:121].Your aunt has $500,000 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. What is the maximum number of $45,000 withdrawals that she can make and still have at least $50,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.) [121: .(4.10) Years to deplete ann. dueC JAnswer: c MEDIUMBEGIN ModeI/YR5.5%PV$500,000PMT$45,000FV$50,000N15.05N rounded15]

a.13b.14c.15d.16e.17

(4.10) Int. rate implicit: annuityC JAnswer: b MEDIUM[endnoteRef:122].Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 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. [122: .(4.10) Int. rate implicit: annuityC JAnswer: b MEDIUMN20PV$2,550,000PMT$250,000FV$0.00I/YR7.49%]

a.7.12%b.7.49%c.7.87%d.8.26%e.8.67%

(4.10) Int. rate implicit: annuityC JAnswer: a MEDIUM[endnoteRef:123].Your girlfriend just won the Florida lottery. She has the choice of $15,000,000 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? [123: .(4.10) Int. rate implicit: annuityC JAnswer: a MEDIUMN20PV$15,000,000PMT$1,050,000FV$0.00I/YR3.44%]

a.3.44%b.3.79%c.4.17%d.4.58%e.5.04%

(4.10) Int. rate implicit: annuity dueC JAnswer: e MEDIUM[endnoteRef:124].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 $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment? [124: .(4.10) Int. rate implicit: annuity dueC JAnswer: e MEDIUMBEGIN ModeN12PV$120,000PMT$15,000FV$0.00I/YR8.41%]

a.6.85%b.7.21%c.7.59%d.7.99%e.8.41%

(4.11) Payments on a perpetuityC JAnswer: b MEDIUM[endnoteRef:125].What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250? [125: .(4.11) Payments on a perpetuityC JAnswer: b MEDIUMCost (PV)$1,250I/YR6.5%PMT$81.25Multiply Cost by I/YR.]

a.$77.19b.$81.25c.$85.31d.$89.58e.$94.06

(4.12) PV of uneven cash flowsC JAnswer: e MEDIUM[endnoteRef:126].What is the present value of the following cash flow stream at a rate of 6.25%? [126: .(4.12) PV of uneven cash flowsC JAnswer: e MEDIUMI/YR = 6.25%01234CFs:$0$75$225$0$300PV of CFs:$0$71$199$0$235PV = $505.30PV = $505.30You 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.]

Years:01234|||||CFs:$0$75$225$0$300

a.$411.57b.$433.23c.$456.03d.$480.03e.$505.30

(4.12) PV of uneven cash flowsC JAnswer: c MEDIUM[endnoteRef:127].What is the present value of the following cash flow stream at a rate of 12.0%? [127: .(4.12) PV of uneven cash flowsC JAnswer: c MEDIUMI/YR = 12.0%01234CFs:$0$1,500$3,000$4,500$6,000PV of CFs:$0$1,339$2,392$3,203$3,813PV = $10,747Found using the Excel NPV function.PV = $10,747Found by summing individual PVs.PV = $10,747Found using the calculator NPV key.]

Years:01234|||||CFs:$0$1,500$3,000$4,500$6,000

a.$9,699b.$10,210c.$10,747d.$11,284e.$11,849

(4.12) PV of uneven cash flowsC JAnswer: d MEDIUM[endnoteRef:128].What is the present value of the following cash flow stream at a rate of 8.0%? [128: .(4.12) PV of uneven cash flowsC JAnswer: d MEDIUMI/YR = 8.0%0123CFs:$750$2,450$3,175$4,400PV of CFs:$750$2,269$2,722$3,493PV = $9,233Found by summing individual PVs.PV = $9,233Found with a calculator or Excel to automate the process. With a calculator, input the cash flows and I into the cash flow register, then press the NPV key.]

Years:0123||||CFs:$750$2,450$3,175$4,400

a.$7,917b.$8,333c.$8,772d.$9,233e.$9,695

(4.12) PV of uneven cash flowsC JAnswer: a MEDIUM[endnoteRef:129].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 6.0%? [129: .(4.12) PV of uneven cash flowsC JAnswer: a MEDIUMI/YR = 6.0%01234CFs:$0$1,000$2,000$2,000$2,000PV of CFs:$0$943$1,780$1,679$1,584PV = $5,987Found using the Excel NPV function.PV = $5,987Found by summing individual PVs.PV = $5,987Found using the calculator NPV key.]

Years:01234|||||CFs:$0$1,000$2,000$2,000$2,000

a.$5,987b.$6,286c.$6,600d.$6,930e.$7,277(4.13) FV of uneven cash flowsC JAnswer: e MEDIUM[endnoteRef:130].At a rate of 6.5%, what is the future value of the following cash flow stream? [130: .(4.13) FV of uneven cash flowsC JAnswer: e MEDIUMI/YR = 6.5%01234CFs:$0$75$225$0$300FV of CFs:$0$91$255$0$300FV = $645.80Found by summing individual FVs.FV = $645.80Found with the NFV key in some calculators.FV = $645.80Found with a calculator by first finding the PV of the stream, then finding the FV of that PV.PV of the stream:$501.99FV of the PV:$645.80]

Years:01234|||||CFs:$0$75$225$0$300

a.$526.01b.$553.69c.$582.83d.$613.51e.$645.80(4.14) Rate in uneven cash flowsC JAnswer: c MEDIUM[endnoteRef:131].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 $10,000 at the end of the 5th year. What is the expected rate of return on this investment? [131: .(4.14) Rate in uneven cash flowsC JAnswer: c MEDIUM012345CFs:-$10,000$750$750$750$750$750$10,000-$10,000$750$750$750$750$10,750I/YR7.50%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.]

a.6.77%b.7.13%c.7.50%d.7.88%e.8.27%

(4.14) Rate in uneven cash flowsC JAnswer: e MEDIUM[endnoteRef:132].You are offered a chance to buy an asset for $7,250 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? [132: .(4.14) Rate in uneven cash flowsC JAnswer: e MEDIUM01234CFs:-$7,250$750$1,000$850$6,250I/YR6.05%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.]

a.4.93%b.5.19%c.5.46%d.5.75%e.6.05%

(4.15) FV, semiannual compoundingC JAnswer: c MEDIUM[endnoteRef:133].Whats the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually? [133: .(4.15) FV, semiannual compoundingC JAnswer: c MEDIUMYears5Periods/Yr2Nom. I/YR6.0%N = Periods10PMT$0I = I/Period3.0%PV$1,500Could be found using a calculator, an equation, or Excel.FV = $2,016Note that we must first convert to periods and rate per period.]

a.$1,819b.$1,915c.$2,016d.$2,117e.$2,223

(4.15) FV, semiannual compoundingC JAnswer: d MEDIUM[endnoteRef:134].Whats the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually? [134: .(4.15) FV, semiannual compoundingC JAnswer: d MEDIUMYears5Periods/Yr2Nom. I/YR4.5%FV$4,500N = Periods10PMT$0I = I/Period2.25%Could be found using a calculator, the equation, or Excel.PV = $3,602Note that we must first convert to periods and rate per period.]

a.$3,089b.$3,251c.$3,422d.$3,602e.$3,782

(4.15) FV, monthly compoundingC JAnswer: b MEDIUM[endnoteRef:135].Whats the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly? [135: .(4.15) FV, monthly compoundingC JAnswer: b MEDIUMYears5Periods/Yr12Nom. I/YR6.0%N = Periods60PMT$0I/Period0.5%PV$1,200Could be found using a calculator, the equation, or Excel.FV$1,618.62Note that we must first convert to periods and rate per period.]

a.$1,537.69b.$1,618.62c.$1,699.55d.$1,784.53e.$1,873.76

(4.15) PV, monthly compoundingC JAnswer: d MEDIUM[endnoteRef:136].Whats the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly? [136: .(4.15) PV, monthly compoundingC JAnswer: d MEDIUMYears5Periods/Yr12Nom. I/YR6.0%N=Periods60PMT$0I/Period0.5%FV$1,525PV = $1,131 = FV/(1+rPer)NPV = $1,131Found using a calculator or Excel]

a.$969b.$1,020c.$1,074d.$1,131e.$1,187

(4.15) APR vs. EFF%C JAnswer: b MEDIUM[endnoteRef:137].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 18.00%, with interest paid monthly, what is the card's EFF%? [137: .(4.15) APR vs. EFF%C JAnswer: b MEDIUMAPR = Nominal rate18.00%Periods/yr12EFF% =(1+(rNOM/N))N 1 =19.56%]

a.18.58%b.19.56%c.20.54%d.21.57%e.22.65%

(4.15) Comparing EFF%C JAnswer: d MEDIUM[endnoteRef:138].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 7.0%, 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? [138: .(4.15) Comparing EFF%C JAnswer: d MEDIUMThis 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, Riverside6.5%Nominal rate, Midwest7.0%Periods/yr, Riverside12Periods/yr, Midwest1EFF% Riverside = (1+(rNOM/N))N 1 =6.70%EFF% Midwest7.00%Difference0.30%]

a.0.52%b.0.44%c.0.36%d.0.30%e.0.24%

(4.15) Nominal rate vs. EFF%C JAnswer: a MEDIUM[endnoteRef:139].Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, 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? [139: .(4.15) Nominal rate vs. EFF%C JAnswer: a MEDIUMNominal I/YR8.00%Periods/yr4EFF% = (1+(rNOM/N))N 1= 8.24%You could also find the EFF% as follows:Interest paid each quarter = Loan rate/4 = Qtrly PMT = $200.00Then find the IRR as a quarterly rate and convert to an annual rate. This procedure is obviously longer.01234CFs:10,000.00-200.00-200.00-200.00-200.00-10,000.0010,000.00-200.00-200.00-200.00-10,200.00IRR (quarterly) = 2.00%Annual effective rate = 8.24% vs. nominal rate = 8.00%]

a.8.24%b.8.45%c.8.66%d.8.88%e.9.10%

(4.15) Nominal rate vs. EFF%C JAnswer: e MEDIUM[endnoteRef:140].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 $250.00 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? [140: .(4.15) Nominal rate vs. EFF%C JAnswer: e MEDIUMInterest payment: $250.0001234CFs:10,000-250-250-250-250-10,00010,000-250-250-250-10,250IRR (quarterly) = 2.50%Annual effective rate = 10.38% vs. nominal rate = 10.00%]

a.8.46%b.8.90%c.9.37%d.9.86%e.10.38%

(4.15) Nominal rate vs. EFF%C JAnswer: c MEDIUM[endnoteRef:141].Pacific Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay? [141: .(4.15) Nominal rate vs. EFF%C JAnswer: c MEDIUMNominal I/YR4.50%Periods/yr12Periodic rate0.38%EFF% = (1+(rNOM/N))N 1 =4.59%]

a.3.72%b.4.13%c.4.59%d.5.05%e.5.56%

(4.15) Nominal rate vs. EFF%C JAnswer: b MEDIUM[endnoteRef:142].Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate? [142: .(4.15) Nominal rate vs. EFF%C JAnswer: b MEDIUMNominal I/YR = APR15.00%Periods/yr12EFF% = (1+(rNOM/N))N 1 =16.08%]

a.15.27%b.16.08%c.16.88%d.17.72%e.18.61%

(4.16) Simple interestC JAnswer: a MEDIUM[endnoteRef:143].Pasco Co. borrowed $20,000 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 Pasco have to pay in a 30-day month? [143: .(4.16) Simple interestC JAnswer: a MEDIUMNominal I/YR7.25%Days in month30Days/yr360Daily rate0.020139%Amount borrowed$20,000Interest per day$4.02778Interest per month = Interest/day 30 =$120.83]

a.$120.83b.$126.88c.$133.22d.$139.88e.$146.87

(4.16) Fractional time periodsC JAnswer: a MEDIUM[endnoteRef:144].Suppose you deposited $5,000 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? [144: .(4.16) Fractional time periodsC JAnswer: a MEDIUMNominal I/YR5.25%Rate/day = rNOM/360 =0.0146%Number of months8Days = Months 30 =240Days in year360Days in month30Amount deposited$5,000Ending amount$5,178.09]

a.$5,178.09b.$5,436.99c.$5,708.84d.$5,994.28e.$6,294.00

(4.17) Amortization: paymentC JAnswer: a MEDIUM[endnoteRef:145].Suppose you borrowed $12,000 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? [145: .(4.17) Amortization: paymentC JAnswer: a MEDIUMYears = N4I/YR9.0%FV$0Amount borrowed = PV$12,000Payments = PMT$3,704.02Found with a calculator, as the PMT.]

a.$3,704.02b.$3,889.23c.$4,083.69d.$4,287.87e.$4,502.26

(4.17) Amortization: paymentC JAnswer: c MEDIUM[endnoteRef:146].Suppose you are buying your first condo for $145,000, 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? [146: .(4.17) Amortization: paymentC JAnswer: c MEDIUMYears30N360Payments/year12Periodic rate0.54%Nominal rate6.50%PV$130,000Purchase price$145,000FV$0.00Down payment$15,000PMT$821.69]

a.$741.57b.$780.60c.$821.69d.$862.77e.$905.91

(4.17) Amortization: paymentC JAnswer: e MEDIUM[endnoteRef:147].Your uncle will sell you his bicycle shop for $250,000, 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? [147: .(4.17) Amortization: paymentC JAnswer: e MEDIUMMonthly annuity, so interest must be calculated on a monthly basis.Years4Payments/year12N48Nominal rate6.0%PV$250,000I/period0.5%FV$50,000PMT$4,947.01]

a.$4,029.37b.$4,241.44c.$4,464.67d.$4,699.66e.$4,947.01

(4.17) Amortization: interestC JAnswer: d MEDIUM[endnoteRef:148].Suppose you borrowed $14,000 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? [148: .(4.17) Amortization: interest C JAnswer: d MEDIUMI/YR10.0%Years5Amount borrowed$14,000Interest in Year 1$1,400.00Simply multiply the rate times the amount borrowed.]

a.$1,200.33b.$1,263.50c.$1,330.00d.$1,400.00e.$1,470.00

(4.17) Amortization: interestC JAnswer: d MEDIUM[endnoteRef:149].You plan to borrow $35,000 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? [149: .(4.17) Amortization: interest C JAnswer: d MEDIUMFind the required payment:N7I7.5%PV$35,000FV$0PMT$6,608.01Found with a calculator or Excel.Amortization schedule (first 2 years)YearBeg. BalancePaymentInterestPrincipalEnd. Balance135,000.006,608.012,625.003,983.0131,016.99231,016.996,608.012,326.274,281.7426,735.25]

a.$1,994.49b.$2,099.46c.$2,209.96d.$2,326.27e.$2,442.59

(4.17) Amortization: interestC JAnswer: b MEDIUM[endnoteRef:150].Your bank offers to lend you $100,000 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? [150: .(4.17) Amortization: interest C JAnswer: b MEDIUMFind the required payment:N10I8.5%PV$100,000FV$0PMT$15,241Found with a calculator or Excel.Amortization schedule (first 2 years)YearBeg. BalancePaymentInterestPrincipalEnd. Balance1100,00015,2418,5006,74193,259293,25915,2417,9277,31485,945]

a.$7,531b.$7,927c.$8,323d.$8,740e.$9,177

(Comp.) N, ann. due, monthly comp.C JAnswer: d MEDIUM[endnoteRef:151].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 $250,000? Round fractional months up. [151: .(Comp.) N, ann. due, monthly comp.C JAnswer: d MEDIUMBEGIN ModeI/YR18.0%I/MO1.5%Monthly annuity due, so interest must be calculated on monthly basis. rNOM/12.PV$0PMT$5,000FV$250,000N37.16Rounded up: 38]

a.23b.27c.32d.38e.44

(Comp.) N, ann. due, monthly comp.C JAnswer: b MEDIUM[endnoteRef:152].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 $150,000? [152: .(Comp.) N, ann. due, monthly comp.C JAnswer: b MEDIUMI/YR7.0%I/MO0.583333%Monthly annuity, so interest must be calculated on monthly basisPV$0PMT$3,000FV$150,000N44.0021]

a.39.60b.44.00c.48.40d.53.24e.58.57

(Comp.) Rate, ord. ann., monthly comp.C JAnswer: d MEDIUM[endnoteRef:153].Your childs 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? [153: .(Comp.)Rate, ord. ann., monthly comp.C JAnswer: d MEDIUMN36PV$4,000PMT$137.41FV$0I/MO1.20%Monthly annuity, so interest must be calculated on monthly basisI/YR = I/MO 12 = 14.36%]

a.12.31%b.12.96%c.13.64%d.14.36%e.15.08%

(4.10) N, lifetime vs. yearlyC JAnswer: e MEDIUM/HARD[endnoteRef:154].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 $850, 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? [154: .(4.10) N, lifetime vs. yearlyC JAnswer: e MEDIUM/HARDFind N for an annuity due with the indicated terms to determine how long you must live to make the lifetime subscription worthwhile.BEGIN ModeInterest rate (I/YR)6.0%Annual cost (PMT)$85Lifetime subscription cost (PV)$850Number of payments made (N)14.33]

a.7.48b.8.80c.10.35d.12.18e.14.33

(4.15) Non-annual compoundingC JAnswer: b MEDIUM/HARD[endnoteRef:155].You just deposited $2,500 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? [155: .(4.15) Non-annual compoundingC JAnswer: b MEDIUM/HARDInterest rate4.0%Periods/year4Years onQuartersEndingQuarterly rate1.0%Depositon DepositAmount1st deposit$2,500312$2,817.06 2nd deposit$5,00028$5,414.28 3rd deposit$7,50014$7,804.53 ]

a.$15,234.08b.$16,035.88c.$16,837.67d.$17,679.55e.$18,563.53

(4.15) Comparing EFF%C JAnswer: d MEDIUM/HARD[endnoteRef:156].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 6.0%, 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? [156: .(4.15) Comparing EFF%C JAnswer: d MEDIUM/HARDStudents 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 "6%, quarterly compounding."Nominal rate, Farmers5.0%Periods/yr, Farmers4Nominal rate, Merchants6.0%Periods/yr, Merchants1EFF% Farmers5.09%EFF% Merchants6.00%Difference0.91%]

a.1.56%b.1.30%c.1.09%d.0.91%e.0.72%

(4.17) Amortization: princ. repymt.C JAnswer: b MEDIUM/HARD[endnoteRef:157].Suppose you borrowed $15,000 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? [157: .(4.17) Amortization: princ. repymt.C JAnswer: b MEDIUM/HARDInterest rate8.5%Years5Amount borrowed$15,000Step 1: Find the PMT3,806.49Step 2: Find the 1st year's interest1,275.00Step 3: Subtract the interest from the payment; this is repayment of principal2,531.49]

a.$2,404.91b.$2,531.49c.$2,658.06d.$2,790.96e.$2,930.51

(4.17) Amortization: ending bal.C JAnswer: e MEDIUM/HARD[endnoteRef:158].Suppose you borrowed $15,000 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? [158: .(4.17) Amortization: ending bal.C JAnswer: e MEDIUM/HARDInterest rate8.5%Years5Amount borrowed$15,000Step 1: Find the PMT$3,806.49Step 2: Find the 1st year's interest$1,275.00Step 3: Subtract the interest from the payment; this is repayment of principal$2,531.49Step 4: Subtract the repayment of principal from the beginning amount owed$12,468.51]

a.$10,155.68b.$10,690.19c.$11,252.83d.$11,845.09e.$12,468.51

(Comp.) Retirement planningC JAnswer: c MEDIUM/HARD[endnoteRef:159].Your sister turned 35 today, and she is planning to save $7,000 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. [159: .(Comp.) Retirement planningC JAnswer: c MEDIUM/HARDInterest rate7.5%Years to retirement30Years in retirement25Amount saved per year$7,000Step 1: Find the amount at age 65; use the FV function723,796Step 2: Find the PMT for a 25-year ordinary annuity using the FV you just found as the PV.64,932]

a.$58,601b.$61,686c.$64,932d.$68,179e.$71,588

(4.10) Finding I in annuity dueC JAnswer: a HARD[endnoteRef:160].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 $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning? [160: .(4.10) Finding I in annuity dueC JAnswer: a HARDBEGIN ModeN24PV$0PMT$500FV$13,000I/MO0.63%I/YR7.62%]

a.7.62%b.8.00%c.8.40%d.8.82%e.9.26%

(4.17) AmortizationC JAnswer: e HARD[endnoteRef:161].Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal? [161: .(4.17) AmortizationC JAnswer: e HARDN12rNOM 11.0%Per. r0.9167%PV$72,500PMT$6,407.67FV$0% prin. = Prin2/PMT = 90.45%Amortization schedule(first 4 months)MonthBeg. BalancePaymentInterestPrincipalEnding Balance172,500.006,407.67664.585,743.0966,756.91266,756.916,407.67611.945,795.7360,961.18360,961.186,407.67558.815,848.8655,112.32455,112.326,407.67505.205,902.4749,209.85]

a.73.67%b.77.55%c.81.63%d.85.93%e.90.45%

(4.17) Amortization: interestC JAnswer: a HARD[endnoteRef:162].On January 1, 2009, your brother's business obtained a 30-year amortized mortgage loan for $250,000 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? [162: .(4.17) Amortization: interestC JAnswer: a HARDYears30Nominal r7.00%Periods/yr12I/period0.5833%N (12 mo.)360PMT$1,663.26PV = Loan$250,000Interest, 2009$17,419.55FV$0Amortization s