Chapter 04
Future Value, Present Value and Interest Rates
Multiple-Choice Questions
1. A promise of a $100 payment to be received one year from today is:
a. more valuable than receiving the payment today.
b. less valuable than receiving the payment two years from now.
c. equally valuable as a payment received today if the interest rate is zero.
d. not enough information is provided to answer the question.
2. The future value of $100 at a 5% per year interest rate at the end of one year is:
a. $95.00
b. $105.00
c. $97.50
d. 107.50
3. Credit:
a. probably came into being at the same time as coinage.
b. predates coinage by 2,000 years.
c. did not exist until the middle ages.
d. first became popular due to the writings of Aristotle.
4. Which of the following expresses 5.65%?
a. 0.565
b. 0.00565
c. 5.65
d. 0.0565
5. Which of the following expresses 4.85%?
a. 0.0485
b. 4.850
c. 0.00485
d. 0.485
6. Which of the following expresses 5.5%?
a. 0.0055
b. 5.50
c. 0.550
d. 0.0550
7. If the interest rate is zero, a promise to receive a $100 payment one year from now is:
a. more valuable than receiving $100 today.
b. less valuable than receiving $100 today.
c. equal in value to receiving $100 today.
d. equal in value to receiving $101 today.
8. If a saver has a positive rate of time preference then the present value of $100 to be received 1
year from today is:
a. more than $100.
b. not calculable.
c. less than 100.
d. unknown to the saver.
9. Which of the following best expresses the proceeds a lender receives from a one-year simple
loan when the annual interest rate equals i?
a. PV + i
b. FV/i
c. PV(1 + i)
d. PV/i
10. Suppose Tom receives a one-year loan from ABC Bank for $5,000.00. At the end of the year,
Tom repays $5,400.00 to ABC Bank. Assuming the simple calculation of interest, the interest rate
on Tom’s loan was:
a. $400
b. 8.00%
c. 7.41%
d. 20%
11. Suppose Mary receives an $8,000 loan from First National Bank. Mary repays $8,480 to First
National Bank at the end of one year. Assuming the simple calculation of interest, the interest rate
on Mary’s loan was:
a. 8.00%
b. $480
c. 6.00%
d. 5.66%
12. An investor deposits $400 into a bank account that earns an annual interest rate of 8%. Based
on this information, how much interest will he earn during the second year alone?
a. $25.60
b. $32
c. $34.56
d. $64
13. Compound interest means that:
a. you get an interest deduction for paying your loan off early.
b. you get interest on interest.
c. you get an interest deduction if you take out a loan for longer than one year.
d. interest rates will rise on larger loans.
14. Which of the following best expresses the payment a saver receives for investing their money
for two years?
a. PV + PV
b. PV + PV (1 + i)
c. PV(1 + i)2
d. 2PV(1 + i)
15. Suppose a family wants to save $60,000 for a child’s tuition. The child will be attending
college in 18 years. For simplicity, assume the family is saving for a one-time college tuition
payment. If the interest rate is 6%, then about how much does this family need to deposit in the
bank today?
a. $10,000
b. $21,000
c. $42,000
d. $57,000
16. Which of the following best expresses the payment a lender receives for lending money for
three years?
a. 3PV
b. PV/(1+i)3
c. PV/(1 + i)3
d. FV/ (1 + i)3
17. Suppose Paul borrows $4,000 for one year from his grandfather who charges Paul 7%
interest. At the end of the year Paul will have to repay his grandfather:
a. $4,280
b. $4,290
c. $4,350
d. $4,820
18. Suppose that Stephen Curry, a basketball player for the Golden State Warriors, will become a
free agent at the end of this NBA season. Suppose that Curry is considering two possible contracts
from different teams. Note that the salaries are paid at the end of EACH year.
Contract #1 (Boston)
Contract #2 (Portland)
Signing bonus (paid today)
$1 million
$1 million
First-year salary
$2 million
$4 million
Second-year salary
$4 million
$4 million
Third-year salary
$5 million
$3 million
The interest rate is 10%. Based on this information, which of the following is true?
a. Curry should take the Boston contract because it has a higher present value.
b. Curry should take the Portland contract because it has a higher present value.
c. Curry is indifferent between the two contracts because they are both worth $12 million.
d. Curry is indifferent between the two contracts because they are both worth $10.9 million.
19. Farou invests $2,000 at 8% interest. About how long will it take for Farou to double his
investment (e.g., to have $4,000)?
a. 4 years
b. 5 years
c. 8 years
d. 9 years
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20. A lender is promised a $100 payment (including interest) one year from today. If the lender
has a 6% opportunity cost of money, he/she should be willing to accept what amount today?
a. $100.00
b. $106.20
c. $96.40
d. $94.34
21. A saver knows that if she put $95 in the bank today she will receive $100 from the bank one
year from now, including the interest she will earn. What is the interest rate she is earning?
a. 5.10%
b. 6.00%
c. 5.52%
d. 5.26%
22. Tom deposits funds in his savings account at the bank which is paying 3.5% interest. If he
keeps his funds in the bank for one year he will have $155.25. What amount is Tom depositing?
a. $151.75
b. $150.00
c. $148.75
d. $147.50
23. Mary deposits funds into a CD at her bank. The CD has an annual interest of 4.0%. If Mary
leaves the funds in the CD for two years she will have $540.80. What amount is Mary depositing?
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a. $520.00
b. $514.50
c. $500.00
d. $512.40
24. Mary deposits funds into a CD at her bank. The CD has an annual interest of 4.0%. If Mary
leaves the funds in the CD for two years she will have $540.80. Assuming no penalties for
withdrawing the funds early, what amount would Mary have at the end of one year?
a. $521.60
b. $490.00
c. $500.00
d. $520.00
25. Sharon deposits $150.00 in her savings account at the bank. At the end of one year she has
$156.38. What was the interest rate that Sharon earned?
a. 4.25%
b. 6.38%
c. 4.52%
d. 5.63%
26. The value of $100 left in a savings account earning 5% a year, will be worth what amount
after ten years?
a. $150.00
b. $160.50
c. $159.84
d. $162.89
27. The value of $100 left in a certificate of deposit for four years that earns 4.5% annually will
be:
a. $120.00
b. $119.25
c. $117.00
d. $145.00
28. The future value of $100 that earns 10% annually for n years is best expressed by which of the
following?
a. $100(0.1)n
b. $100 × n × (1.1)
c. $100(1.1)n
d. $100/(1.1)n
29. The future value of $200 that is left in account earning 6.5% interest for three years is best
expressed by which of the following?
a. $200(1.065) × 3
b. $200(1.065)/3
c. $200(1.065)n
d. $200(1.065)3
30. Which of the following best expresses the future value of $100 left in a savings account
earning 3.5% for three and a half years?
a. $100(1.035)3.5
b. $100(0.35)3.5
c. $100 × 3.5 × (1.035)
d. $100(1.035)3/2
31. Which of the following best expresses the present value of $500 that you have to wait four
years and three months to receive?
a. ($500/4.25) × (1 + i)
b. $500 × 4.25 × (1 + i)
c. $500/(1 + i)4.25
d. ($500/4) × (1 + i)3
32. If 10% is the annual rate, considering compounding, the monthly rate is:
a. 0.0833%
b. 0.833%
c. 0.80%
d. 1.0833%
33. What is the future value of $1,000 after six months earning 12% annually?
a. $1,050.00
b. $1,060.00
c. $1,120.00
d. $1,058.30
34. In reading the national business news, you hear that mortgage rates increased by 50 basis
points. If mortgage rates were initially at 6.5%, what are they after this increase?
a. 6.55%
b. 7.0%
c. 11.5%
d. 56.5%
35. One hundred basis points could be expressed as:
a. 0.01%
b. 1.00%
c. 100.0%
d. 0.10%
36. The decimal equivalent of a basis point is:
a. 0.0001
b. 1.00
c. 0.001
d. 0.01
37. According to the rule of 72:
a. any amount should double in value in 72 months if invested at 10%.
b. 72/interest rate is the number of years approximately it will take for an amount to double.
c. 72 × interest rate is the number of years it will take for an amount to double.
d. the interest rate divided by the number of years invested will always equal 72%.
38. The rule of 72 says that at 6% interest $100 should become $200 in about:
a. 72 months
b. 100 months
c. 12 years
d. 7.2 years
39. What is the present value of $200 promised two years from now at 5% annual interest?
a. $190.00
b. $220.00
c. $180.00
d. $181.41
40. What is the present value of $100 promised one year from now at 10% annual interest?
a. $89.50
b. $90.00
c. $90.91
d. $91.25
41. What is the present value of $500 promised four years from now at 5% annual interest?
a. $411.35
b. $400.00
c. $607.75
d. $520.00
42. The higher the future value of the payment the:
a. lower the present value.
b. higher the present value.
c. future value doesn’t impact the present value, only the interest rate really matters.
d. lower the present value because the interest rate must fall.
43. The shorter the time until a payment the:
a. higher the present value.
b. lower the present value because time is valuable.
c. lower must be the interest rate.
d. higher must be the interest rate.
44. The lower the interest rate, i, the:
a. lower is the present value.
b. greater must be n.
c. higher is the present value.
d. higher is the future value.
45. Doubling the future value will cause:
a. the present value to fall by half.
b. the interest rate, i, to double.
c. no change to present value, only the interest rate.
d. the present value to double.
46. Doubling the future value will cause the:
a. present value to double.
b. present value to decrease.
c. present value to increase by less than 100%.
d. interest rate, i, to decrease.
47. The present value and the interest rate have:
a. a direct relationship; as i increases, pv increases.
b. an inverse relationship; as i increases, pv decreases.
c. an unclear relationship; whether it is direct or inverse depends on the interest rate.
d. no relationship.
48. At any fixed interest rate, an increase in time, n, until a payment is made:
a. increases the present value.
b. has no impact on the present value since the interest rate is fixed.
c. reduces the present value.
d. affects only the future value.
49. A change in the interest rate:
a. has a smaller impact on the present value of a payment to be made far into the future than on
one to be made sooner.
b. will not make a difference in the present values of two equal payments to be made at different
times.
c. has a larger impact on the present value of a payment to be made far into the future than on one
to be made sooner.
d. has a larger impact on the present value of a bigger payment to be made far into the future than
on one of lesser value.
50. A monthly growth rate of 0.5% is an annual growth rate of:
a. 6.00%
b. 5.00%
c. 6.17%
d. 6.50%
51. A monthly growth rate of 0.6% is an annual growth rate of:
a. 7.20%
b. 6.00%
c. 7.60%
d. 7.44%
52. A monthly interest rate of 1% is a compounded annual rate of :
a. 12.68%
b. 10.00%
c. 14.11%
d. 6.00%
53. An investment has grown from $100.00 to $130.00 or by 30% over four years. What annual
increase gives a 30% increase over four years?
a. 7.50%
b. 6.30%
c. 6.78%
d. 7.24%
54. An investment grows from $100.00 to $150.00 or 50% over five years. What annual increase
gives a 50% increase over five years?
a. 12.00%
b. 10.00%
c. 9.25%
d. 8.45%
55. The “coupon rate” is:
a. the annual amount of interest payments made on a bond as a percentage of the amount
borrowed.
b. the change in the value of a bond expressed as a percentage of the amount borrowed.
c. another name for the yield on a bond, assuming the bond is sold before it matures.
d. the total amount of interest payments made on a bond as a percentage of the amount borrowed.
56. Higher savings usually requires higher interest rates because:
a. everyone prefers to save more instead of consuming.
b. saving requires sacrifice and people must be compensated for this sacrifice.
c. higher savings means we expect interest rates to decrease.
d. of the rule of 72.
57. The internal rate of return of an investment is:
a. the same as return on investment.
b. zero when the present value of an investment equals its cost.
c. the interest rate that equates the present value of an investment with its cost.
d. equal to the market rate of interest when an investment is made.
58. If the internal rate of return from an investment is more than the opportunity cost of funds the
firm should:
a. make the investment.
b. not make the investment.
c. only make the investment using retained earnings.
d. only make part of the investment and wait to see if interest rates decrease.
59. A mortgage, where the monthly payments are the same for the duration of the loan, is an
example of a(n):
a. variable payment loan.
b. installment loan.
c. fixed payment loan.
d. equity security.
60. An investment carrying a current cost of $120,000 is going to generate $50,000 of revenue for
each of the next three years. To calculate the internal rate of return we need to:
a. calculate the present value of each of the $50,000 payments and multiply these and set this equal
to $120,000.
b. find the interest rate at which the present value of $150,000 for three years from now equals
$120,000.
c. find the interest rate at which the sum of the present values of $50,000 for each of the next three
years equals $120,000.
d. subtract $120,000 from $150,000 and set this difference equal to the interest rate.
61. Usually an investment will be profitable if:
a. the internal rate of return is less than the cost of borrowing.
b. the cost of borrowing is equal to the internal rate of return.
c. it is financed with retained earnings.
d. the cost of borrowing is less than the internal rate of return.
62. A coupon bond is a bond that:
a. always sells at a price that is less than the face value.
b. provides the owner with regular payments.
c. pays the owner the sum of the coupons at the bond’s maturity.
d. pays a variable coupon rate depending on the bond’s price.