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Chapter 28: Time Value of Money
ANSWER:
True
42. 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.
a.
True
b.
False
ANSWER:
False
43. 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).
a.
True
b.
False
ANSWER:
True
44. 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).
a.
True
b.
False
ANSWER:
False
45. Your bank account pays a 5% nominal rate of interest. The interest is compounded quarterly. Which of the following
statements is CORRECT?
a.
The periodic rate of interest is 5% and the effective rate of interest is also 5%.
b.
The periodic rate of interest is 1.25% and the effective rate of interest is 2.5%.
c.
The periodic rate of interest is 5% and the effective rate of interest is greater than 5%.
d.
The periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%.
e.
The periodic rate of interest is 2.5% and the effective rate of interest is 5%.
ANSWER:
d
46. Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following
statements is CORRECT?
a.
The periodic rate of interest is 8% and the effective rate of interest is also 8%.
b.
The periodic rate of interest is 2% and the effective rate of interest is 4%.
c.
The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.
d.
The periodic rate of interest is 4% and the effective rate of interest is less than 8%.
e.
The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.
ANSWER:
e
47. At the end of 10 years, which of the following investments would have the highest future 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 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).
ANSWER:
a
48. Of the following investments, which 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).
ANSWER:
d
49. 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 PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity.
b.
The periodic interest rate is greater than 3%.
c.
The periodic rate is less than 3%.
d.
The present value would be greater if the lump sum were discounted back for more periods.
e.
The present value of the $1,000 would be smaller if interest were compounded monthly rather than
semiannually.
ANSWER:
e
50. 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 PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity.
b.
The periodic interest rate is greater than 3%.
c.
The periodic rate is less than 3%.
d.
The present value would be greater if the lump sum were discounted back for more periods.
e.
The present value of the $1,000 would be larger if interest were compounded monthly rather than
semiannually.
ANSWER:
a
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51. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?
a.
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.
b.
The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.
c.
A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year
mortgage.
d.
A bank loan's nominal interest rate will always be equal to or less than its effective annual rate.
e.
If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.
ANSWER:
d
52. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?
a.
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 28: Time Value of Money
b.
The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.
c.
A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year
mortgage.
d.
A bank loan's nominal interest rate will always be equal to or greater than its effective annual rate.
e.
If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%.
ANSWER:
e
53. Which of the following statements is CORRECT?
a.
An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is
smaller than 6%.
b.
The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary
annuity.
c.
If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.
d.
If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all
be different.
e.
The proportion of the payment that goes toward interest on a fully amortized loan increases over time.
ANSWER:
b
54. Which of the following statements is CORRECT?
a.
An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is
smaller than 6%.
b.
The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity
due.
c.
If a loan has a nominal annual rate of 7%, then the effective rate will never be less than 7%.
d.
If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all
be different.
e.
The proportion of the payment that goes toward interest on a fully amortized loan increases over time.
ANSWER:
c
55. Which of the following bank accounts has the highest effective annual return?
a.
An account that pays 8% nominal interest with daily (365-day) compounding.
b.
An account that pays 8% nominal interest with monthly compounding.
c.
An account that pays 8% nominal interest with annual compounding.
d.
An account that pays 7% nominal interest with daily (365-day) compounding.
e.
An account that pays 7% nominal interest with monthly compounding.
ANSWER:
a
56. Which of the following bank accounts has the lowest effective annual return?
a.
An account that pays 8% nominal interest with daily (365-day) compounding.
b.
An account that pays 8% nominal interest with monthly compounding.
c.
An account that pays 8% nominal interest with annual compounding.
d.
An account that pays 7% nominal interest with daily (365-day) compounding.
e.
An account that pays 7% nominal interest with monthly compounding.
ANSWER:
e
57. 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.
ANSWER:
e
58. What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?
a.
$1,819
b.
$1,915
c.
$2,016
d.
$2,117
e.
$2,223
ANSWER:
c
59. What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded
semiannually?
a.
$3,089
b.
$3,251
c.
$3,422
d.
$3,602
e.
$3,782
ANSWER:
d
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60. What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?
a.
$1,537.69
b.
$1,618.62
c.
$1,699.55
d.
$1,784.53
e.
$1,873.76
ANSWER:
b
61. What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded
Chapter 28: Time Value of Money
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Page 33
monthly?
a.
$969
b.
$1,020
c.
$1,074
d.
$1,131
e.
$1,187
ANSWER:
d
62. American Express 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%?
a.
18.58%
b.
19.56%
c.
20.54%
d.
21.57%
e.
22.65%
63. Southwestern 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. Woodburn 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 Woodburn versus the rate charged by Southwestern?
a.
0.52%
b.
0.44%
c.
0.36%
d.
0.30%
e.
0.24%
POINTS:
1
64. 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?
a.
8.24%
b.
8.45%
c.
8.66%
d.
8.88%
e.
9.10%
POINTS:
1
65. Suppose People's 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?
a.
8.46%
b.
8.90%
c.
9.37%
d.
9.86%
e.
10.38%
ANSWER:
e
66. Pacific Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%)
does the bank pay?
a.
3.72%
b.
4.13%
c.
4.59%
d.
5.05%
e.
5.56%
POINTS:
1
67. 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?
a.
15.27%
b.
16.08%
c.
16.88%
d.
17.72%
e.
18.61%
POINTS:
1
68. 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?
a.
$15,234.08
b.
$16,035.88
c.
$16,837.67
d.
$17,679.55
e.
$18,563.53
ANSWER:
b
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69. Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. An
offer to lend you the $50,000 also comes from Community Bank, 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?
a.
1.56%
b.
1.30%
c.
1.09%
d.
0.91%
e.
0.72%
ANSWER:
d
70. A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.
a.
True
b.
False
Chapter 28: Time Value of Money
ANSWER:
True
71. A "growing annuity" is any cash flow stream that grows over time.
a.
True
b.
False
ANSWER:
False
72. You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9
more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect
to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be
to enable you to reach your $50,000 target?
a.
$3,008
b.
$3,342
c.
$3,676
d.
$4,044
e.
$4,448
ANSWER:
b
Chapter 28: Time Value of Money
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Page 40
POINTS:
1
