CHAPTER 28—TIME VALUE OF MONEY
1. Starting to invest early for retirement increases the benefits of compound interest.
a.
True
b.
False
True
Compounding
2. Starting to invest early for retirement reduces the benefits of compound interest.
a.
True
b.
False
False
Compounding
3. A time line is meaningful even if all cash flows do not occur annually.
a.
True
b.
False
True
Compounding
4. A time line is not meaningful unless all cash flows occur annually.
a.
True
b.
False
False
CHAPTER 28—TIME VALUE OF MONEY
5. Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.
a.
True
b.
False
True
Compounding
6. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.
a.
True
b.
False
False
Compounding
7. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.
a.
True
b.
False
True
Compounding
CHAPTER 28—TIME VALUE OF MONEY
Compounding
8. Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.
a.
True
b.
False
False
Difficulty: Easy
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Compounding
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.
a.
True
b.
False
True
Difficulty: Easy
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Compounding
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.
a.
True
b.
False
False
Difficulty: Easy
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Compounding
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.
CHAPTER 28—TIME VALUE OF MONEY
a.
True
b.
False
False
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.
a.
True
b.
False
True
13. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future
value.
a.
True
b.
False
True
14. Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present
value.
a.
True
b.
False
CHAPTER 28—TIME VALUE OF MONEY
False
15. If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.
a.
True
b.
False
False
16. If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.
a.
True
b.
False
True
17. A “growing annuity” is a cash flow stream that grows at a constant rate for a specified number of periods.
a.
True
b.
False
True
CHAPTER 28—TIME VALUE OF MONEY
18. A “growing annuity” is any cash flow stream that grows over time.
a.
True
b.
False
False
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.
a.
True
b.
False
False
Compounding
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.
a.
True
b.
False
True
Compounding
CHAPTER 28—TIME VALUE OF MONEY
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.)
a.
True
b.
False
True
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.)
a.
True
b.
False
False
23. The present value of a future sum decreases as either the discount rate or the number of periods per year increases,
CHAPTER 28—TIME VALUE OF MONEY
other things held constant.
a.
True
b.
False
True
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.
a.
True
b.
False
False
25. 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
True
26. All other things held constant, the present value of a given annual annuity increases as the number of periods per year
CHAPTER 28—TIME VALUE OF MONEY
increases.
a.
True
b.
False
False
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.
a.
True
b.
False
True
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.
a.
True
b.
False
False
29. As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than
CHAPTER 28—TIME VALUE OF MONEY
the nominal rate on the deposit (or loan).
a.
True
b.
False
True
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).
a.
True
b.
False
False
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.
a.
True
b.
False
False
Amortization
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.
a.
True
b.
False
CHAPTER 28—TIME VALUE OF MONEY
True
Amortization
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.
a.
True
b.
False
True
Amortization
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.
a.
True
b.
False
False
Amortization
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.
a.
True
b.
False
CHAPTER 28—TIME VALUE OF MONEY
False
Amortization
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.
a.
True
b.
False
True
CHAPTER 28—TIME VALUE OF MONEY
37. Which of the following statements is CORRECT?
a.
Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven
amounts.
b.
A time line is not meaningful unless all cash flows occur annually.
c.
Time lines are useful for visualizing complex problems prior to doing actual calculations.
d.
Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur
quarterly.
e.
Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods.
Difficulty: Moderate
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Time lines
TYPE: Multiple Choice: Conceptual
38. Which of the following statements is CORRECT?
a.
Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven
amounts.
b.
A time line is not meaningful unless all cash flows occur annually.
c.
Time lines are not useful for visualizing complex problems prior to doing actual calculations.
d.
Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur
quarterly.
e.
Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the
periods.
Difficulty: Moderate
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Time lines
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CHAPTER 28—TIME VALUE OF MONEY
39. Which of the following statements is CORRECT?
a.
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.
b.
A time line is not meaningful unless all cash flows occur annually.
c.
Time lines are not useful for visualizing complex problems prior to doing actual calculations.
d.
Time lines can be constructed to deal with situations where some of the cash flows occur annually but others
occur quarterly.
e.
Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for
ordinary annuities.
Difficulty: Moderate
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Time lines
TYPE: Multiple Choice: Conceptual
calculations. Please see the “Answers & Solutions” section to see calculation requirements
for this question.
40. Which of the following statements is CORRECT?
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.
Difficulty: Moderate
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TYPE: Multiple Choice: Conceptual
for this question.
CHAPTER 28—TIME VALUE OF MONEY
Time lines
TYPE: Multiple Choice: Conceptual
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?
a.
The discount rate decreases.
b.
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.
c.
The discount rate increases.
d.
The riskiness of the investment’s cash flows decreases.
e.
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.
Difficulty: Moderate
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Effects of factors on PVs
TYPE: Multiple Choice: Conceptual
for this question.
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?
a.
The discount rate increases.
b.
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.
c.
The discount rate decreases.
d.
The riskiness of the investment’s cash flows increases.
e.
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.
Difficulty: Moderate
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CHAPTER 28—TIME VALUE OF MONEY
43. Which of the following statements is CORRECT?
a.
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.
b.
The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
c.
If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition
an annuity.
d.
The cash flows for an annuity due must all occur at the ends of the periods.
e.
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.
Difficulty: Moderate
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TYPE: Multiple Choice: Conceptual
44. Which of the following statements is CORRECT?
a.
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.
b.
The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
c.
If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition
an annuity.
d.
The cash flows for an annuity due must all occur at the beginning of the periods.
e.
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.
Difficulty: Moderate
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Effects of factors on PVs
TYPE: Multiple Choice: Conceptual
CHAPTER 28—TIME VALUE OF MONEY
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%.
Difficulty: Moderate
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TYPE: Multiple Choice: Conceptual
for this question.
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%.
Difficulty: Moderate
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Quarterly compounding
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TYPE: Multiple Choice: Conceptual
CHAPTER 28—TIME VALUE OF MONEY
47. 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.
Difficulty: Moderate
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TYPE: Multiple Choice: Conceptual
calculations. Please see the “Answers & Solutions” section to see calculation requirements
48. 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.
TYPE: Multiple Choice: Conceptual
for this question.
CHAPTER 28—TIME VALUE OF MONEY
49. Which of the following statements regarding a 20-year (240-month) $225,000, fixed-rate mortgage is CORRECT?
(Ignore taxes and transactions costs.)
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.
Difficulty: Moderate
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TYPE: Multiple Choice: Conceptual
for this question.
50. 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.
Difficulty: Moderate
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TYPE: Multiple Choice: Conceptual
for this question.
CHAPTER 28—TIME VALUE OF MONEY
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.
Difficulty: Moderate
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TYPE: Multiple Choice: Conceptual
51. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest
rate of 8% is CORRECT?
a.
Exactly 8% of the first monthly payment represents interest.
b.
The monthly payments will decline over time.
c.
A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal,
than for the first monthly payment.
d.
The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.
e.
The amount representing interest in the first payment would be higher if the nominal interest rate were 6%
rather than 8%.
Difficulty: Moderate
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