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Chapter 05: Time Value of Money
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.
50. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest
rate of 10% is CORRECT?
a.
The monthly payments will increase over time.
b.
A larger proportion of the first monthly payment will be interest, and a smaller proportion will be principal,
Chapter 05: Time Value of Money
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.
51. Which of the following investments would have the highest future value at the end of 10 years? Assume that the
effective annual rate for all investments is the same and is greater than zero.
a.
Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
b.
Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
c.
Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20
payments).
d.
Investment D pays $2,500 at the end of 10 years (just one payment).
e.
Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).
Chapter 05: Time Value of Money
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).
53. A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%,
semiannual compounding. Which of the following statements is CORRECT?
a.
The periodic interest rate is greater than 3%.
b.
The periodic rate is less than 3%.
c.
The present value would be greater if the lump sum were discounted back for more periods.
d.
The present value of the $1,000 would be smaller if interest were compounded monthly rather than
semiannually.
e.
The PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity.
Chapter 05: Time Value of Money
54. A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%,
semiannual compounding. Which of the following statements is CORRECT?
a.
The periodic interest rate is greater than 3%.
b.
The periodic rate is less than 3%.
c.
The present value would be greater if the lump sum were discounted back for more periods.
d.
The present value of the $1,000 would be larger if interest were compounded monthly rather than
semiannually.
e.
The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity.
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.
Chapter 05: Time Value of Money
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.
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%.
Chapter 05: Time Value of Money
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.
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.
Chapter 05: Time Value of Money
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.
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.
Chapter 05: Time Value of Money
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.
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.
Chapter 05: Time Value of Money
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.
65. You plan to invest some money in a bank account. Which of the following banks provides you with the highest
effective rate of interest?
a.
Bank 1; 6.1% with annual compounding.
b.
Bank 2; 6.0% with monthly compounding.
c.
Bank 3; 6.0% with annual compounding.
d.
Bank 4; 6.0% with quarterly compounding.
e.
Bank 5; 6.0% with daily (365-day) compounding.
Chapter 05: Time Value of Money
Multiple Choice: Problems
66. Sue now has $280. How much would she have after 8 years if she leaves it invested at 8.5% with annual
compounding?
a.
$537.77
b.
$462.48
c.
$473.24
d.
$639.95
e.
$510.88
Chapter 05: Time Value of Money
67. Jose now has $500. How much would he have after 6 years if he leaves it invested at 6.7% with annual compounding?
a.
$855.88
b.
$752.59
c.
$568.13
d.
$737.83
e.
$885.40
68. Suppose you have $2,350 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest,
compounded annually. How much will you have when the CD matures?
a.
$2,539.87
b.
$2,791.06
c.
$2,428.22
d.
$3,488.83
e.
$3,153.90
Chapter 05: Time Value of Money
69. Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 11.4% interest,
compounded annually. How much will you have when the CD matures?
a.
$6,063.44
b.
$5,886.84
c.
$5,357.02
d.
$7,299.68
e.
$6,769.86
Chapter 05: Time Value of Money
70. Last year Rocco Corporation's sales were $175 million. If sales grow at 6% per year, how large (in millions) will they
be 5 years later?
a.
$290.39
b.
$281.03
c.
$271.66
d.
$196.72
e.
$234.19
71. Last year Dania Corporation's sales were $525 million. If sales grow at 9.5% per year, how large (in millions) will
they be 8 years later?
a.
$965.74
b.
$1,085.11
c.
$1,204.47
d.
$976.60
e.
$1,020.00
Chapter 05: Time Value of Money
72. How much would $1, growing at 12.1% per year, be worth after 75 years?
a.
$6,041.14
b.
$5,253.16
c.
$6,408.86
d.
$4,465.19
e.
$5,095.57
73. How much would $100, growing at 5% per year, be worth after 65 years?
a.
$1,787.99
b.
$2,717.75
c.
$2,383.99
d.
$2,574.71
Chapter 05: Time Value of Money
e.
$2,860.79
74. You deposit $1,125 today in a savings account that pays 6% interest, compounded annually. How much will your
account be worth at the end of 25 years?
a.
$5,842.31
b.
$4,876.64
c.
$5,456.04
d.
$4,828.35
e.
$3,669.55
Chapter 05: Time Value of Money
75. You deposit $500 today in a savings account that pays 6% interest, compounded annually. How much will your
account be worth at the end of 20 years?
a.
$1,539.43
b.
$1,747.89
c.
$1,908.25
d.
$1,699.78
e.
$1,603.57
76. Suppose a State of New York bond will pay $1,000 ten years from now. If the going interest rate on these 10-year
bonds is 4.9%, how much is the bond worth today?
a.
$619.79
b.
$464.84
c.
$669.37
d.
$625.99
e.
$650.78
Chapter 05: Time Value of Money
77. 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 6.2%, how much is the bond worth today?
a.
$537.68
b.
$704.54
c.
$618.02
d.
$673.64
e.
$741.63
Chapter 05: Time Value of Money
78. How much would $30,000 due in 50 years be worth today if the discount rate were 7.5%?
a.
$838.94
b.
$959.94
c.
$621.14
d.
$806.67
e.
$613.07
79. How much would $5,000 due in 25 years be worth today if the discount rate were 5.5%?
a.
$1,101.38
b.
$1,311.17
c.
$983.38
d.
$1,232.50
e.
$1,166.94
Chapter 05: Time Value of Money
80. Suppose a U.S. treasury bond will pay $1,700 five years from now. If the going interest rate on 5-year treasury bonds
is 4.25%, how much is the bond worth today?
a.
$1,380.60
b.
$1,035.45
c.
$1,698.14
d.
$1,090.68
e.
$1,711.95
81. Suppose an Exxon Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year
bonds is 5.60%, how much is the bond worth today?
a.
$3,001.04
b.
$2,609.60
Chapter 05: Time Value of Money
c.
$2,139.87
d.
$2,218.16
e.
$2,948.84
82. Suppose the U.S. Treasury offers to sell you a bond for $597.25. No payments will be made until the bond matures 5
years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond
at the offer price?
a.
9.01%
b.
9.56%
c.
11.08%
d.
11.94%
e.
10.86%
