Chapter 05: Time Value of Money
Note that there is an overlap between the T/F and multiple-choice questions, as some of the T/F statements are used in
multiple-choice questions.
Multiple Choice: True/False
1. Starting to invest early for retirement increases the benefits of compound interest.
a.
True
b.
False
True
EASY
Compounding
2. Starting to invest early for retirement reduces the benefits of compound interest.
a.
True
b.
False
False
EASY
Compounding
3. A time line is meaningful even if all cash flows do not occur annually.
a.
True
b.
False
True
EASY
Chapter 05: Time Value of Money
4. A time line is not meaningful unless all cash flows occur annually.
a.
True
b.
False
False
EASY
Compounding
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
EASY
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
EASY
Compounding
Chapter 05: Time Value of Money
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
EASY
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
EASY
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
EASY
Compounding
Chapter 05: Time Value of Money
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
EASY
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.
a.
True
b.
False
False
EASY
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
Compounding
Chapter 05: Time Value of Money
b.
False
True
EASY
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
EASY
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
False
EASY
Chapter 05: Time Value of Money
15. If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.
a.
True
b.
False
False
EASY
5-16 Comparing Interest Rates
16. If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.
a.
True
b.
False
True
EASY
5-16 Comparing Interest Rates
17. 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
MODERATE
Compounding
Chapter 05: Time Value of Money
18. 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
MODERATE
5-2 Future Values
True / False
FOFM.BRIG.17.05.02 – Future Values
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Compounding
Bloom’s: Comprehension
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19. 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
MODERATE
5-2 Future Values
True / False
FOFM.BRIG.17.05.02 – Future Values
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Comparative compounding
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20. 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.)
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Chapter 05: Time Value of Money
a.
True
b.
False
False
MODERATE
21. The present value of a future sum decreases as either the discount rate or the number of periods per year increases,
other things held constant.
a.
True
b.
False
MODERATE
22. 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
MODERATE
Chapter 05: Time Value of Money
23. 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
MODERATE
24. 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
False
MODERATE
Chapter 05: Time Value of Money
25. 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
MODERATE
5-15 Semiannual and Other Compounding Periods
26. 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
MODERATE
5-15 Semiannual and Other Compounding Periods
27. 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
True
MODERATE
5-16 Comparing Interest Rates
Chapter 05: Time Value of Money
28. 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
MODERATE
5-16 Comparing Interest Rates
29. 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
MODERATE
5-18 Amortized Loans
Amortization
30. 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
True
MODERATE
5-18 Amortized Loans
Chapter 05: Time Value of Money
31. 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
MODERATE
5-18 Amortized Loans
Amortization
32. 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
MODERATE
5-18 Amortized Loans
Amortization
33. 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
Amortization
Chapter 05: Time Value of Money
b.
False
False
$1,000
$1,000
Rate
10%
Rate
41.45%
Payment
$402.11
Payment
$640.98
Beg.
End.
Beg.
End.
Balance
Interest
Principal
Bal.
Balance
Interest
Principal
Bal.
$1,000.00
$100.00
$302.11
$697.89
$1,000.00
$414.50
$226.48
$773.52
$697.89
$69.79
$332.33
$365.56
$773.52
$320.62
$320.36
$453.15
$365.56
$36.56
$365.56
$0.00
$453.15
$187.83
$453.15
$0.00
CHALLENGING
5-18 Amortized Loans
Amortization
34. 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
$1,000
$1,000
Rate
10%
Rate
41.45%
Payment
$402.11
Payment
$640.98
Beg.
End.
Beg.
End.
$1,000.00
$100.00
$302.11
$697.89
$1,000.00
$414.50
$226.48
$773.52
$697.89
$69.79
$332.33
$365.56
$773.52
$320.62
$320.36
$453.15
Chapter 05: Time Value of Money
Multiple Choice: Conceptual
Please note that some of the answer choices, or answers that are very close, are used in different questions. This has
caused us no difficulties, but please take this into account when you make up exams.
35. Which of the following statements is CORRECT?
a.
A time line is not meaningful unless all cash flows occur annually.
b.
Time lines are useful for visualizing complex problems prior to doing actual calculations.
c.
Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur
quarterly.
d.
Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods.
e.
Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven
amounts.
MODERATE
5-1 Time Lines
Multiple Choice
Conceptual
FOFM.BRIG.17.05.01 – Time Lines
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Time lines
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36. 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 in situations where some of the cash flows occur annually but others occur
quarterly.
d.
Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the
$365.56
$36.56
$365.56
$0.00
$453.15
$187.83
$453.15
$0.00
CHALLENGING
5-18 Amortized Loans
True / False
FOFM.BRIG.17.05.18 – Amortized Loans
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Amortization
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Chapter 05: Time Value of Money
periods.
e.
Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven
amounts.
MODERATE
5-1 Time Lines
Multiple Choice
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Time lines
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37. 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 can 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 cannot be constructed where some of the payments constitute an annuity but others are unequal and
thus are not part of the annuity.
c
MODERATE
5-1 Time Lines
Multiple Choice
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Time lines
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38. 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.
Chapter 05: Time Value of Money
5-1 Time Lines
Multiple Choice
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Time lines
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39. 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 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.
b.
The discount rate increases.
c.
The riskiness of the investment’s cash flows decreases.
d.
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.
e.
The discount rate decreases.
5-3 Present Values
Multiple Choice
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Effects of factors on PVs
Bloom’s: Analysis
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40. 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 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.
b.
The discount rate decreases.
c.
The riskiness of the investment’s cash flows increases.
d.
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.
e.
The discount rate increases.
5-3 Present Values
Chapter 05: Time Value of Money
41. Which of the following statements is CORRECT?
a.
The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
b.
If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition
an annuity.
c.
The cash flows for an annuity due must all occur at the ends of the periods.
d.
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.
e.
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.
5-6 Annuities
Multiple Choice
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42. Which of the following statements is CORRECT?
a.
The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
b.
If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition
an annuity.
c.
The cash flows for an annuity due must all occur at the beginning of the periods.
d.
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.
e.
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.
5-6 Annuities
Multiple Choice
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Effects of factors on PVs
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Chapter 05: Time Value of Money
43. Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following
statements is CORRECT?
a.
The periodic rate of interest is 1.5% and the effective rate of interest is 3%.
b.
The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.
c.
The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.
d.
The periodic rate of interest is 3% and the effective rate of interest is 6%.
e.
The periodic rate of interest is 6% and the effective rate of interest is also 6%.
Multiple Choice
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Quarterly compounding
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44. 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 2% and the effective rate of interest is 4%.
b.
The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.
c.
The periodic rate of interest is 4% and the effective rate of interest is less than 8%.
d.
The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.
e.
The periodic rate of interest is 8% and the effective rate of interest is also 8%.
Multiple Choice
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Quarterly compounding
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Chapter 05: Time Value of Money
45. A $50,000 loan is to be amortized over 7 years, with annual end–of-year payments. Which of these statements is
CORRECT?
a.
The annual payments would be larger if the interest rate were lower.
b.
If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either
case, the first payment would include more dollars of interest under the 7-year amortization plan.
c.
The proportion of each payment that represents interest as opposed to repayment of principal would be lower
if the interest rate were lower.
d.
The last payment would have a higher proportion of interest than the first payment.
e.
The proportion of interest versus principal repayment would be the same for each of the 7 payments.
Multiple Choice
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46. A $150,000 loan is to be amortized over 7 years, with annual end–of-year payments. Which of these statements is
CORRECT?
a.
The annual payments would be larger if the interest rate were lower.
b.
If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either
case, the first payment would include more dollars of interest under the 7-year amortization plan.
c.
The proportion of each payment that represents interest as opposed to repayment of principal would be higher
if the interest rate were lower.
d.
The proportion of each payment that represents interest versus repayment of principal would be higher if the
interest rate were higher.
e.
The proportion of interest versus principal repayment would be the same for each of the 7 payments.
FOFM.BRIG.17.05.18 – Amortized Loans
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Chapter 05: Time Value of Money
47. 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 it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal
payments) are constant.
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 slower rate in the later years of the loan’s life.
eliminated. One could also set up an amortization schedule to prove that only statement b is
Multiple Choice
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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.
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