CHAPTER 2
TIME VALUE OF MONEY
(Difficulty: E = Easy, M = Medium, and T = Tough)
Note: Most problems assume students have a calculator with a yx feature (i.e., an exponential feature).
Annuity problems for finding the
...
CHAPTER 2
TIME VALUE OF MONEY
(Difficulty: E = Easy, M = Medium, and T = Tough)
Note: Most problems assume students have a calculator with a yx feature (i.e., an exponential feature).
Annuity problems for finding the interest rate or the number of periods are in the financial calculator
section at the end of this chapter.
Multiple Choice: Conceptual
Easy:
PV and discount rate
1
. 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.
PV versus FV
2
. Which of the following statements is most correct?
a. 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.
b. To increase present consumption beyond present income normally requires either the
payment of interest or else an opportunity cost of interest foregone.
c. 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.
d. Disregarding risk, if the present value of a sum is equal to its future value, either k = 0 or t =
0.
e. Each of the statements above is true.
Time value concepts
3
. Which of the following statements is most correct?
a. A 5-year $100 annuity due will have a higher present value than a 5- year $100 ordinary
annuity.
b. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same
amount and same interest rate.
c. If an investment pays 10 percent interest compounded annually, its effective rate will also be
10 percent.
d. Statements a and c are correct.
e. All of the statements above are correct.
Chapter 2 - Page 1Time value concepts
4
. The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is
10 percent and interest is compounded semiannually. Which of the following statements is most
correct?
a. The present value of the $1,000 is greater if interest is compounded monthly rather than
semiannually.
b. The effective annual rate is greater than 10 percent.
c. The periodic interest rate is 5 percent.
d. Both statements b and c are correct.
e. All of the statements above are correct.
Time value concepts
5
. Which of the following statements is most correct?
a. The present value of an annuity due will exceed the present value of an ordinary annuity
(assuming all else equal).
b. The future value of an annuity due will exceed the future value of an ordinary annuity
(assuming all else equal).
c. The nominal interest rate will always be greater than or equal to the effective annual interest
rate.
d. Statements a and b are correct.
e. All of the statements above are correct.
Effective annual rate
6
. Which of the following statements is most correct?
a. If annual compounding is used, the effective annual rate equals the nominal rate.
b. If annual compounding is used, the effective annual rate equals the periodic rate.
c. If a loan has a 12 percent nominal rate with semiannual compounding, its effective annual
rate is equal to 11.66 percent.
d. Answers a and b are correct.
e. Answers a and c are correct.
7
. Which of the following bank accounts has the highest effective annual return?
a. An account which pays 10 percent nominal interest with monthly com-pounding.
b. An account which pays 10 percent nominal interest with daily com-pounding.
c. An account which pays 10 percent nominal interest with annual com-pounding.
d. An account which pays 9 percent nominal interest with daily com-pounding.
e. All of the investments above have the same effective annual return.
Effective annual rate
8
. You are interested in investing your money in a bank account. Which of the following banks
provides you with the highest effective rate of interest?
a. Bank 1; 8 percent with monthly compounding.
b. Bank 2; 8 percent with annual compounding.
c. Bank 3; 8 percent with quarterly compounding.
d. Bank 4; 8 percent with daily (365-day) compounding.
e. Bank 5; 7.8 percent with annual compounding.
Chapter 2 - Page 2Amortization
9
. Your family recently obtained a 30-year (360-month) $100,000 fixed-rate mortgage. Which of the
following statements is most correct? (Ignore all taxes and transactions costs.)
a. The remaining balance after three years will be $100,000 less the total amount of interest
paid during the first 36 months.
b. The proportion of the monthly payment that goes towards repayment of principal will be
higher ten years from now than it will be this year.
c. The monthly payment on the mortgage will steadily decline over time.
d. All of the statements above are correct.
e. None of the statements above is correct.
Amortization
10
. Frank Lewis has a 30-year, $100,000 mortgage with a nominal interest rate of 10 percent and
monthly compounding. Which of the following statements regarding his mortgage is most
correct?
a. The monthly payments will decline over time.
b. The proportion of the monthly payment which represents interest will be lower for the last
payment than for the first payment on the loan.
c. The total dollar amount of principal being paid off each month gets larger as the loan
approaches maturity.
d. Statements a and c are correct.
e. Statements b and c are correct.
Medium:
Annuities Answer: c Diff: M
11
. Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per
year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which
of the following statements is most correct?
a. The present value of the ordinary annuity must exceed the present value of the annuity due,
but the future value of an ordinary annuity may be less than the future value of the annuity
due.
b. The present value of the annuity due exceeds the present value of the ordinary annuity, while
the future value of the annuity due is less than the future value of the ordinary annuity.
c. The present value of the annuity due exceeds the present value of the ordinary annuity, and
the future value of the annuity due also exceeds the future value of the ordinary annuity.
d. If interest rates increase, the difference between the present value of the ordinary annuity and
the present value of the annuity due remains the same.
e. Answers a and d are correct.
Chapter 2 - Page 3Time value concepts
12
. 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 most 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.
Time value concepts
13
. Which of the following is most correct?
a. The present value of a 5-year annuity due will exceed the present value of a 5-year ordinary
annuity. (Assume that both annuities pay $100 per period and there is no chance of default.)
b. If a loan has a nominal rate of 10 percent, then the effective rate can never b
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