# CHAPTER 6 TIME VALUE OF MONEY Tr by wuyunyi

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```									                                          CHAPTER 6
TIME VALUE OF MONEY

True-False     (Difficulty: E = Easy, M = Medium, and T = Tough)

PV versus FV
1
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

2
Disregarding risk, if money has time value, it is impossible for the present value of a
given sum to be greater than its future value.

a. True
b. False

3
Disregarding risk, if money has time value, the future value of some amount of money
will always be more than the amount originally invested, and the present value of some
amount to be received in the future is always less than that future amount to be received.

a. True
b. False

Discounting process
4
The process of discounting or finding the present value of a cash flow to be received in
the future is really the reverse of compounding.

a. True
b. False

Loan amortization
5
The payment made each period on an amortized loan is constant, and it consists of some
interest and some principal. The later we are in the loan's life, the larger the principal
portion of the payment.

a. True
b. False
Effective annual rate
6
If a bank uses quarterly compounding for savings accounts, the nominal rate (APR) will
be greater than the effective annual rate.

a. True
b. False

Opportunity cost rate
7
The opportunity cost rate is only applicable if you as an investor actually have an
alternative investment to compare. If you are making a decision about a single
investment, the opportunity rate concept does not apply.

a. True
b. False

PV of a sum
8
The present value of a future sum decreases as either the discount rate or the number of
discount periods per year increases.

a. True
b. False

Periodic and nominal rates
9
If we calculate a periodic interest rate, say a monthly rate, in order to get the nominal
annual rate (APR), we can multiply the periodic rate by the number of periods within a
year.

a. True
b. False

Interest factors
10
For all positive interest rates, FVIFk,n 1.0 and PVIFAk,n n.

a. True
b. False

Tabular and calculator methods
11
Financial calculator and tabular methods use different mathematical formulas to solve
time value of money problems, and that is why they always lead to different results.

a. True
b. False
Multiple Choice: Conceptual

PV of a sum
12
Given some amount to be received several years in the future, if the interest rate
increases, the present value of the future amount will be

a.   Higher.
b.   Lower.
c.   Stay the same.
d.   Cannot tell.
e.   Variable.

PV and discount rate
13
You have determined the profitability of a planned project by finding the present value
of all the cash flows from 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.

Multiple Choice: Problems

Time for a sum to double
14
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 nominal 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
FV of an annuity
15
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

PV of an annuity
16
What is the present value of a 5-year ordinary annuity with annual payments of \$200,
evaluated at a 15 percent interest rate?

a.   \$ 670.43
b.   \$ 842.91
c.   \$1,169.56
d.   \$1,348.48
e.   \$1,522.64

Annuity payments
17
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

PV of an uneven CF stream
18
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 Year 9, with 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 value of these cash
flows?

a.   \$ 9,851
b.   \$13,250
c.   \$11,714
d.   \$15,129
e.   \$17,353
Finding PMT
19
Suppose the present value of a 2-year ordinary annuity is \$100. If the discount rate is 10
percent, what must be the annual cash flow?

a.   \$65.45
b.   \$82.64
c.   \$57.62
d.   \$53.78
e.   \$79.22

Quarterly compounding
20
If \$100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will
it be worth in 5 years? a.      \$122.02         b.    \$105.10        c.    \$135.41        d.       \$120.90
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