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Chapter 28: Time Value of Money
STATE STANDARDS:
United States - AK - DISC: Time value of money
73. Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is
invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year, how much can she withdraw (to the
nearest dollar) at the beginning of each year and keep the withdrawals constant in real terms, i.e., growing at the same rate
as inflation and thus enabling her to maintain a constant standard of living?
a.
$65,632
b.
$72,925
c.
$81,027
d.
$89,130
e.
$98,043
ANSWER:
c
Chapter 28: Time Value of Money
POINTS:
1
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Page 43
74. Scott and Linda have been saving to pay for their daughter Casie's college education. Casie just turned 10 at (t = 0),
and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500
a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years⎯if she takes longer or
wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school
year (at t = 8, 9, 10, and 11).
So far, Scott and Linda have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan
is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual
contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large
must the annual payments at t = 5, 6, and 7 be to cover Casie's anticipated college costs?
a.
$1,965.21
b.
$2,068.64
c.
$2,177.51
d.
$2,292.12
e.
$2,412.76
Chapter 28: Time Value of Money
POINTS:
1
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Page 45
75. All other things held constant, the present value of a given annual annuity decreases as the number of periods per year
increases.
a.
True
b.
False
ANSWER:
True
76. All other things held constant, the present value of a given annual annuity increases as the number of periods per year
increases.
a.
True
b.
False
ANSWER:
False
77. You are considering two equally risky annuities, each of which pays $15,000 per year for 20 years. Investment ORD
is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is
Chapter 28: Time Value of Money
CORRECT?
a.
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.
b.
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.
c.
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.
d.
The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the
future value of DUE.
e.
The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the
future value of ORD.
ANSWER:
e
78. You are considering two equally risky annuities, each of which pays $25,000 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.
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.
b.
A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ.
c.
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.
d.
The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the
future value of DUE.
e.
The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the
future value of ORD.
ANSWER:
b
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79. What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?
a.
$16,576
b.
$17,449
c.
$18,367
d.
$19,334
e.
$20,352
ANSWER:
e
80. What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?
a.
$16,806
b.
$17,690
c.
$18,621
d.
$19,601
Chapter 28: Time Value of Money
e.
$20,633
ANSWER:
e
81. Your friend offers to pay you an annuity of $2,500 at the end of each year for 3 years in return for cash today. You
could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?
a.
$5,493.71
b.
$5,782.85
c.
$6,087.21
d.
$6,407.59
e.
$6,744.83
ANSWER:
e
82. After receiving a reward for information leading to the arrest of a notorious criminal, you are considering investing it
in 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?
a.
$50,753
b.
$53,424
c.
$56,236
d.
$59,195
e.
$62,311
ANSWER:
e
83. An uncle of yours who is about to retire wants to sell some of his stock and buy an annuity that will provide him 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 him to buy such an annuity today?
a.
$574,924
b.
$605,183
c.
$635,442
d.
$667,214
e.
$700,575
ANSWER:
b
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84. What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?
a.
$11,262.88
b.
$11,826.02
c.
$12,417.32
d.
$13,038.19
e.
$13,690.10
ANSWER:
a
85. A new investment opportunity for you is 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?
Chapter 28: Time Value of Money
a.
$1,412.84
b.
$1,487.20
c.
$1,565.48
d.
$1,643.75
e.
$1,725.94
ANSWER:
c
86. Your father is considering purchasing an annuity that pays $5,000 at the beginning of each year for 5 years. He could
earn 4.5% on his money in other investments with equal risk. What is the most he should pay for the annuity?
a.
20,701
b.
$21,791
c.
$22,938
d.
$24,085
e.
$25,289
ANSWER:
c
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87. Because your mother is about to retire, she wants to buy an annuity that will provide her 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 her to buy the annuity today?
a.
$825,835
b.
$869,300
c.
$915,052
d.
$963,213
e.
$1,011,374
ANSWER:
d
88. Now that your uncle has decided to retire, 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?
a.
$1,063,968
b.
$1,119,966
c.
$1,178,912
d.
$1,240,960
Chapter 28: Time Value of Money
e.
$1,303,008
ANSWER:
d
89. A salt mine you inherited 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 mine is 7.5%, how much should you ask for it if you decide to sell it?
a.
$284,595
b.
$299,574
c.
$314,553
d.
$330,281
e.
$346,795
ANSWER:
b
90. Geraldine was injured in a car accident, and the insurance company has offered her 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 her as well off financially as with the annuity?
a.
$225,367
b.
$237,229
c.
$249,090
d.
$261,545
e.
$274,622
ANSWER:
b
91. What's 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%?
a.
$8,509
b.
$8,957
c.
$9,428
d.
$9,924
e.
$10,446
ANSWER:
e
92. 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.
a.
True
b.
False
ANSWER:
False
93. 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.
a.
True
b.
False
ANSWER:
True
94. 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.
a.
True
b.
False
ANSWER:
True
95. 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.
a.
True
b.
False
ANSWER:
False
96. 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.
a.
True
b.
False
ANSWER:
False
97. 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.
a.
True
b.
False
ANSWER:
True
98. A $250,000 loan is to be amortized over 8 years, with annual end-of-year payments. Which of these statements is
CORRECT?
a.
The proportion of interest versus principal repayment would be the same for each of the 8 payments.
b.
The annual payments would be larger if the interest rate were lower.
c.
If the loan were amortized over 10 years rather than 8 years, and if the interest rate were the same in either
case, the first payment would include more dollars of interest under the 8-year amortization plan.
d.
The proportion of each payment that represents interest as opposed to repayment of principal would be lower
if the interest rate were lower.
e.
The last payment would have a higher proportion of interest than the first payment.
ANSWER:
d
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99. A $150,000 loan is to be amortized over 6 years, with annual end-of-year payments. Which of these statements is
CORRECT?
a.
The proportion of interest versus principal repayment would be the same for each of the 7 payments.
b.
The annual payments would be larger if the interest rate were lower.
c.
If the loan were amortized over 10 years rather than 6 years, and if the interest rate were the same in either
case, the first payment would include more dollars of interest under the 6-year amortization plan.
d.
The proportion of each payment that represents interest as opposed to repayment of principal would be higher
if the interest rate were lower.
e.
The proportion of each payment that represents interest versus repayment of principal would be higher if the
interest rate were higher.
ANSWER:
e
100. Which of the following statements regarding a 20-year (240-month) $225,000, fixed-rate mortgage is CORRECT?
(Ignore taxes and transactions costs.)
Chapter 28: Time Value of Money
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a.
The outstanding balance declines at a slower rate in the later years of the loan's life.
b.
The remaining balance after three years will be $225,000 less one third of the interest paid during the first
three years.
c.
Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal
payments) are constant.
d.
Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will
remain constant.
e.
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.
ANSWER:
c
101. Which of the following statements regarding a 15-year (180-month) $225,000, fixed-rate mortgage is CORRECT?
(Ignore taxes and transactions costs.)
a.
The outstanding balance declines at a faster rate in the later years of the loan's life.
b.
The remaining balance after three years will be $125,000 less one third of the interest paid during the first
three years.
c.
Because the outstanding balance declines over time, the monthly payments will also decline over time.
d.
Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will
remain constant.
e.
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.
ANSWER:
a
