Chapter 05: Time Value of Money
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48. 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’s life.
49. 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.
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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).
52. 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).
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55. 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.
56. 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.
57. 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.
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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%.
58. 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%.
59. 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.
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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.
60. 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.
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61. 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 will be more than 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.
62. 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 will be more than 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.
63. Which of the following bank accounts has the highest effective annual return?
a. An account that pays 8% nominal interest with monthly compounding.
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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.
64. 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.
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e. $1,502.42
69. Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 13.6% interest,
compounded annually. How much will you have when the CD matures?
a. $7,945.78
b. $7,158.36
c. $6,156.19
d. $6,585.69
e. $5,440.35
70. Last year Rocco Corporation’s sales were $600 million. If sales grow at 6% per year, how large (in millions) will they
be 5 years later?
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a. $810.96
b. $722.64
c. $642.35
d. $979.58
e. $802.94
71. Last year Dania Corporation’s sales were $525 million. If sales grow at 10.5% per year, how large (in millions) will
they be 8 years later?
a. $1,073.61
b. $1,166.96
c. $1,295.33
d. $1,015.26
e. $1,225.31
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72. How much would $1, growing at 12.0% per year, be worth after 75 years?
a. $4,863.93
b. $4,913.06
c. $4,716.53
d. $4,077.84
e. $4,126.97
73. How much would $100, growing at 5% per year, be worth after 70 years?
a. $2,616.67
b. $2,799.23
c. $3,042.64
d. $3,499.04
e. $3,073.07
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d. 6.25%
e. 7.92%
84. Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this year were $3.60. What was the growth rate in
earnings per share (EPS) over the 10-year period?
a. 18.99%
b. 23.35%
c. 21.82%
d. 19.64%
e. 24.44%