CFIN4
Chapter 4 – Time Value of Money
1. Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities.
They cannot be used when making decisions about investments in physical assets.
a. True
b. False
2. One of the potential benefits of investing early for retirement is that an investor can receive greater benefits from the
compounding of interest.
a. True
b. False
3. Of all the techniques used in finance, the least important is the concept of the time value of money.
a. True
b. False
4. Compounding is the process of converting today’s values, which are termed present value, to future value.
a. True
b. False
5. The coupon rate is the rate of return you could earn on alternative investments of similar risk.
a. True
b. False
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Chapter 4 – Time Value of Money
6. A perpetuity is an annuity with perpetual payments.
a. True
b. False
7. An amortized loan is a loan that requires equal payments over its life; its payments include both interest and
repayment of the debt.
a. True
b. False
8. The greater the number of compounding periods within a year, the greater the future value of a lump sum invested
initially, and the greater the present value of a given lump sum to be received at maturity.
a. True
b. False
9. Suppose an investor can earn a steady 5% annually with investment A, while investment B will yield a constant 12%
annually. Within 11 years time, the compounded value of investment B will be more than twice the compounded
value of investment A (ignore risk).
a. True
b. False
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Chapter 4 – Time Value of Money
10. Solving for the interest rate associated with a stream of uneven cash flows, without the use of a calculator, usually
involves a trial and error process.
a. True
b. False
11. When a loan is amortized, the largest portion of the periodic payment goes to reduce principal in the early years of
the loan such that the accumulated interest can be spread out over the life of the loan.
a. True
b. False
12. The effective annual rate is always greater than the simple rate as a result of compounding effects.
a. True
b. False
13. Because we usually assume positive interest rates in time value analyses, the present value of a three-year annuity
will always be less than the future value of a single lump sum, if the sum of the annuity payments equals the original
lump sum investment.
a. True
b. False
CFIN4
Chapter 4 – Time Value of Money
14. All else equal, a dollar received sooner is worth more than a dollar received at some later date, because the sooner
the dollar is received the more quickly it can be invested to earn a positive return.
a. True
b. False
15. An annuity is a series of equal payments made at fixed equal-length intervals for a specified number of periods.
a. True
b. False
16. The difference between an ordinary annuity and an annuity due is that each of the payments of the annuity due
earns interest for one additional year (period).
a. True
b. False
17. The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of
the annuity due is discounted by one more year.
a. True
b. False
CFIN4
Chapter 4 – Time Value of Money
18. The effective annual rate is less than the simple rate when we have monthly compounding.
a. True
b. False
19. Given some amount to be received several years in the future, if the interest rate increases, the present value of the
future amount will
a. Be higher.
b. Be lower.
c. Stay the same.
d. Cannot tell.
e. Be variable.
20. You have determined the profitability of a planned project by finding the present value of all the cash flows form that
project. Which of the following would cause the project to look more appealing in terms of the present value of those
cash flows?
a. The discount rate decreases.
b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the
same.
c. The discount rate increases.
d. Answers b and c above.
e. Answers a and b above.
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Chapter 4 – Time Value of Money
21. As the discount rate increases without limit, the present value of the future cash inflows
a. Gets larger without limit.
b. Stays unchanged.
c. Approaches zero.
d. Gets smaller without limit, i.e., approaches minus infinity.
e. Goes to ern.
22. Which of the following statements is most correct?
a. If annual compounding is used, the effective annual rate equals the simple rate.
b. If annual compounding is used, the effective annual rate equals the periodic rate.
c. If a loan has a 12 percent simple rate with semiannual compounding, its effective annual rate is equal to 11.66
percent.
d. Both answers a and b are correct.
e. Both answers a and c are correct.
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Chapter 4 – Time Value of Money
23. Why is the present value of an amount to be received (paid) in the future less than the future amount?
a. Deflation causes investors to lose purchasing power when their dollars are invested for greater than one year.
b. Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a
larger amount in the future.
c. Investments generally are not as good as those who sell them suggest, so investors usually are not willing to
pay full face value for such investments, thus the price is discounted.
d. Because investors are taxed on the income received from investments they never will buy an investment for
the amount expected to be received in the future.
e. None of the above is a correct answer.
24. By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the
costs do not change over time)?
a. ordinary annuity
b. annuity due
c. nonconstant annuity
d. annuity in arrears
25. What is the effective annual return (EAR) for an investment that pays 10 percent compounded annually?
a. equal to 10 percent
b. greater than 10 percent
c. less than 10 percent
d. This question cannot be answered without knowing the dollar amount of the investment.
e. None of the above is correct.
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Chapter 4 – Time Value of Money
26. What is the term used to describe an annuity with an infinite life?
a. perpetuity
b. infinuity
c. infinity due
d. There is no special term for an infinite annuity.
27. Everything else equal, which of the following conditions will result in the lowest present value of an amount to be
received in the future?
a. annual compounding
b. quarterly compounding
c. monthly compounding
d. daily compounding
28. Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years.
One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth-maximizing
investor which annuity would you choose?
a. The annuity due.
b. The deferred annuity.
c. Either one, because as the problem is set up, they have the same present value.
d. Without information about the appropriate interest rate, we cannot find the values of the two annuities, hence
we cannot tell which is better.
e. The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be
preferred.
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Chapter 4 – Time Value of Money
29. Which of the following statements is correct?
a. For all positive values of r and n, FVIFr, n ≥ 1.0 and PVIFAr, n ≥ n.
b. You may use the PVIF tables to find the present value of an uneven series of payments. However, the
PVIFA tables can never be of use, even if some of the payments constitute an annuity (for example, $100
each year for Years 3, 4, and 5), because the entire series does not constitute an annuity.
c. If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective
annual rate.
d. The present value of a future sum decreases as either the simple interest rate or the number of discount
periods per year increases.
e. All of the above statements are false.
30. Which of the following statements is correct?
a. Other things held constant, an increase in the number of discounting periods per year increases the present
value of a given annual annuity.
b. Other things held constant, an increase in the number of discounting periods per year increases the present
value of a lump sum to be received in the future.
c. The payment made each period under an amortized loan is constant, and it consists of some interest and some
principal. The later we are is the loan’s life, the smaller the interest portion of the payment.
d. There is an inverse relationship between the present value interest factor of an annuity and the future value
interest factor of an annuity, (i.e., one is the reciprocal of the other).
e. Each of the above statements is true.
31. A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, 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 5 years, and if the interest rate were the same in either
case, the first payment would include more dollars of interest under the 5-year amortization plan.
c. The last payment would have a higher proportion of interest than the first payment.
d. The proportion of interest versus principal repayment would be the same for each of the 5 payments.
e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher
if the interest rate were higher.
32. Which of the following statements is correct?
a. Simple rates can’t be used in present value or future value calculations because they fail to account for
compounding effects.
b. The periodic interest rate can be used directly in calculations as long as the number of payments per year is
greater than or equal to the number of compounding periods per year.
c. In all cases where interest is added or payments are made more frequently than annually, the periodic rate is
less than the annual rate.
d. Generally, the APR is greater than the EAR as a result of compounding effects.
e. If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by
two.
CFIN4
Chapter 4 – Time Value of Money
33. All else equal, if you expect to receive a certain amount in the future, say, $500 in ten (10) years, the present value
of that future amount will be lowest if the interest earned on such investments is compounded
a. daily
b. weekly
c. monthly
d. quarterly
e. annually
34. Which of the following payments (receipts) would probably not be considered an annuity due? Based on your
knowledge and using logic, think about the timing of the payments.
a. rent payments associated with a five-year lease
b. payments for a magazine subscription for a two-year period where the payments are made annually
c. interest payments associated with a corporate bond that was issued today
d. annual payments associated with lottery winnings that are paid out as an annuity
35. All else equal, the future value of a lump-sum amount invested today will increase if the
a. interest rate that is earned is lowered.
b. number of compounding periods is increased.
c. investment time period is shortened.
d. amount initially invested is lowered.
e. Two or more of the above answers are correct.
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Chapter 4 – Time Value of Money
36. Susan just signed a long-term lease on a townhouse in New York City (near Central Park) that requires her to make
equal monthly payments for the next five years. The payments Susan has promised to make represent a(n)
the landlord.
a. ordinary annuity
b. annuity due
c. series of uneven cash flows
d. perpetuity
37. Suppose that the present value of receiving a guaranteed $450 in two years is $385.80. The opportunity rate of
return on similar risk investments is 8 percent. According to this information, all else equal, which of the following
statements is correct?
a. It always would be preferable to wait two years to receive the $450 because this value is greater than the
present value.
b. Risk averse investors always would prefer to take the $385.80 today because it is a guaranteed amount
whereas there is uncertainty as to whether the future amount will be paid.
c. No investor should be willing to pay more than $385.80 for such an investment.
d. It is apparent the present value was computed incorrectly because the present value of a future amount
always should be greater than the future value.
e. None of the above is a correct answer.
for
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Chapter 4 – Time Value of Money
38. You plan to invest an amount of money in five-year certificate of deposit (CD) at your bank. The stated interest rate
applied to the CD is 12 percent, compounded monthly. How much must you invest if you want the balance in the
CD account to be $8,500 in five years?
a. $4,678.82
b. $4,823.13
c. $13,600.00
d. $14,979.90
e. $7,589.29
39. Vegit Corporation needs to borrow funds to support operations during the summer. Vegit’s CFO is trying to decide
whether to borrow from the Bank of Florida or the Bank of Georgia. The loan offered by Bank of Florida has a 12.5
percent simple interest rate with annual interest payments, whereas the loan offered by the Bank of Georgia has a
12 percent simple interest rate with monthly payments. Which bank should Vegit use for the loan?
a. Bank of Georgia, because the 12 percent simple interest is cheaper than the 12.5 percent simple interest at
Bank of Florida.
b. Bank of Georgia, because the effective interest rate on the loan is less than 12 percent, whereas the effective
interest rate on the loan at the Bank of Florida is greater than 12.5 percent.
c. Bank of Florida, because the simple interest rate is higher, which means that Vegit will be able to invest the
proceeds from the loan at a higher rate of return.
d. Bank of Florida, because the effective interest rate on the loan is 12.5 percent, which is less than the 12.7
percent effective interest rate on the loan offered by the Bank of Georgia.
e. There is not enough information to answer this question.
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Chapter 4 – Time Value of Money
40. Alice’s investment advisor is trying to convince her to purchase an investment that pays $250 per year. The
investment has no maturity; therefore the $250 payment will continue every year forever. Alice has determined that
her required rate of return for such an investment should be 14 percent and that she would hold the investment for
10 years and then sell it. If Alice decides to buy the investment, she would receive the first $250 payment one year
from today. How much should Alice be willing to pay for this investment?
a. $1,304.03, because this is the present value of an ordinary annuity that pays $250 a year for 10 years at 14
percent.
b. $1,486.59, because this is the present value of an annuity due that pays $250 a year for 10 years at 14
percent.
c. $1,785.71, because this is the present value of a $250 perpetuity at 14 percent.
d. There is not enough information to answer this question, because the selling price of the investment in 10
years is not known today.
e. None of the above is correct.
41. At approximately what rate would you have to invest a lump-sum amount today if you need the amount to triple in
six years? Assume interest is compounded annually.
a. 20%
b. 12%
c. 24%
d. Not enough information is provided to answer the question.
e. None of the above is a correct answer.
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Chapter 4 – Time Value of Money
42. Sarah is thinking about purchasing an investment from HiBond Investing. If she buys the investment, Sarah will
receive $100 every three months for five years. The first $100 payment will be made as soon as she purchases the
investment. If Sarah’s required rate of return is 16 percent, to the nearest dollar, how much should she be willing to
pay for this investment?
a. $1,359
b. $1,413
c. $1,112
d. $1,519
e. $1,310
43. Which of the following statements is most correct?
a. The first payment under a 3–year, annual payment, amortized loan for $1,000 will include a smaller percentage
(or fraction) of interest if the interest rate is 5 percent than if it is 10 percent.
b. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent
simple, or quoted, rate but with semiannual payments, rather than at a 10.1 percent simple rate with annual
payments. However, as a borrower you should prefer the annual payment loan.
c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate
the perpetuity approaches zero.
d. Statements a, b, and c are all true.
e. Only statements b and c are true.
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Chapter 4 – Time Value of Money
44. A recent advertisement in the financial section of a magazine carried the following claim: “Invest your money with us
at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine.” Ignoring
taxes, how long would it take to double your money at a simple rate of 14 percent, compounded annually?
a. Approximately 3.5 years
b. Approximately 5 years
c. Exactly 7 years
d. Approximately 10 years
e. Exactly 14 years
45. At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value?
(Round to the closest year.)
a. 5
b. 8
c. 6
d. 10
e. 9
46. You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to
finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski
instructor rather than continue in school, so you close out your account. How much money will you receive?
a. $1,171
b. $1,126
c. $1,082
d. $1,163
e. $1,008
47. What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent
interest rate?
a. $670.44
b. $842.91
c. $1,169.56
d. $1,522.64
e. $1,348.48
48. If a 5-year regular annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of
each annuity payment?
a. $240.42
b. $263.80
c. $300.20
d. $315.38
e. $346.87
49. You have the opportunity to buy a perpetuity which pays $1,000 annually. Your required rate of return on this
investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were
offered at a price of
a. $5,000.00
b. $6,000.00
c. $6,666.67
d. $7,500.00
e. $8,728.50
50. Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Y
all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present val
cash flows?
a. $9,851
b. $13,250
c. $11,714
d. $15,129
e. $17,353
51. If $100 is placed in an account that earns a simple 4 percent, compounded quarterly, what will it be worth in 5 years?
a. $122.02
b. $105.10
c. $135.41
d. $120.90
e. $117.48
52. In 1958 the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average
cost was $13,700. What was the growth rate in tuition over the 30-year period?
a. 12%
b. 9%
c. 6%
d. 7%
e. 8%
53. At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years. How long to the
nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%?
a. 12 years
b. 15 years
c. 18 years
d. 20 years
e. 23 years