Chapter 6—THE TIME VALUE OF MONEY
MULTIPLE CHOICE
1. Other names for the interest rate include all of the following except:
a.
inflation rate
b.
opportunity rate
c.
discount rate
d.
required rate of return
2. The present value of a single amount can be represented as
a.
PV0 = FVn(PVIFi,n)
b.
PV0 = FVn(PVIFAi,n)
c.
PV0 = FVn[1/(1 + i)n]
d.
a and c
3. The basic future value equation is given by
a.
FVn = PV0(PVIFi,n)
b.
FVn = PV0(FVIFAi,n)
c.
FVn = PV0(1/(1+ i)n)
d.
FVn = PV0(FVIFi,n)
4. The process of finding present values is frequently called
a.
annualizing
b.
compounding
c.
discounting
d.
leasing
5. The values shown in ordinary annuity tables (either present value or compound value) can be adjusted
to the annuity due form by ____ the ordinary annuity interest factor by ____.
a.
dividing, (1 + i)
b.
dividing, (1 + i)n
c.
multiplying, (1 + i)
d.
multiplying, (1 + i)n
6. A(n) ____ is a financial instrument that agrees to pay an equal amount of money per period into the
indefinite future (i.e. forever)
a.
annuity
b.
annuity due
c.
sinking fund
d.
perpetuity
7. Finding the discounted current value of $1,000 to be received at the end of each of the next 5 years
requires calculating the
a.
future value of an annuity
b.
future value of an annuity due
c.
present value of an annuity
d.
present value of an annuity due
8. Finding the compound sum of $1,000 to be received at the beginning of each of the next 5 years
requires calculating the
a.
future value of an annuity
b.
present value of an annuity
c.
future value of an annuity due
d.
present value of an annuity due
9. When using a present value of an annuity table(e.g.,Table III at the back of the book),
a.
payments are assumed to be made at the beginning of each period
b.
PVIFA factors decrease with an increase in the interest rate
c.
PVIFA factors increase with an increase in the number of periods
d.
PVIFA factors decrease with an increase in the interest rate and increase with an increase
in the number of periods
10. When using a future value of an annuity table (e.g., Table III at the back of the book),
a.
payments are assumed to be made at the end of each period
b.
FVIFA factors increase with an increase in the interest rate
c.
FVIFA factors increase with an increase in the number of periods
d.
all of these answers are correct
11. An annuity due is one in which
a.
payments or receipts occur at the end of each period.
b.
payments or receipts occur at the beginning of each period.
c.
payments or receipts occur forever.
d.
cash flows occur continuously.
12. You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000.
What will happen to the present value of your winnings if the interest rate increases during the next 20
years?
a.
it will be worth less
b.
it will be worth more
c.
it will not change
d.
none of these answers are correct.
13. You have just calculated the present value of the expected cash flows of a potential investment.
Management thinks your figures are too low. Which of the following actions would improve the
present value of your cash flows?
a.
extend the cash flows over a longer period of time
b.
increase the discount rate
c.
decrease the discount rate
d.
extend the cash flows over a longer period of time and decrease the discount rate
14. If the present value of a given sum is equal to its future value, then
a.
the discount rate must be very high
b.
there is no inflation
c.
the discount rate must be zero
d.
none of these are correct
15. Using the “Rule of 72,” about how long will it take a sum of money to double in value if the annual
interest rate is 9 percent?
a.
9 years
b.
7 years
c.
8 years
d.
10 years
16. The present value of an ordinary annuity is the
a.
sum of the present value of a series of equal periodic payments
b.
future value of an equal series of payments
c.
receipt of equal cash flows for a specified amount of time
d.
sum of the future value of an equal series of payments
17. When a loan is amortized over a five year term, the
a.
rate of interest is reduced each year
b.
amount of interest paid is reduced each year
c.
payment is reduced each year
d.
balance is paid as a balloon payment in the fifth year
18. Annuity due calculations are especially important when dealing with
a.
term loans
b.
lease contracts
c.
capital investments
d.
capital recovery problems
19. The more frequent the compounding, the
a.
greater the present value
b.
greater the amount deposited
c.
greater the effective interest rate
d.
lesser the future value
20. The effective rate of interest will always be ____ the nominal rate.
a.
greater than
b.
equal to
c.
less than
d.
equal to or greater than
21. ____ is interest that is paid not only on the principal, but also on any interest earned but not withdrawn
during earlier periods.
a.
basic interest
b.
simple interest
c.
future interest
d.
compound interest
22. Which of the following is worth more?
a.
Future value of an ordinary annuity of PMT dollars per year for n years discounted at i
percent.
b.
Future value of an annuity due of PMT dollars per year for n years discounted at i percent.
c.
Both are worth the same amount.
d.
Cannot be determined from the information given.
23. The annual effective rate of interest (ieff ) is a function of:
a.
the annual nominal rate of interest (inom)
b.
the number of compounding intervals per year (m)
c.
the number of years (n)
d.
both the annual nominal rate of interest (inom) and the number of compounding intervals
per year (m)
24. More frequent compounding results in ____ future values and ____ present values than less frequent
compounding at the same interest rate.
a.
higher, higher
b.
lower, higher
c.
higher, lower
d.
lower, lower
25. The present value of a(n) ____ is determined by dividing the annual cash flow by the interest rate.
a.
annuity
b.
annuity due
c.
perpetuity
d.
none of these are correct
26. An annuity that begins more than 1 year in the future is referred to as a(n) ____.
a.
perpetuity
b.
annuity due
c.
uneven annuity
d.
deferred annuity
27. The ____ of a perpetual stream of equal, annual returns (PMT) discounted at i% per year is equal to
____.
a.
present value; PMT/i
b.
present value; PMT x i
c.
future value; PMT/i
d.
future value; PMT x i
28. Annuity due calculations are most common when dealing with:
a.
cash dividends
b.
loan repayments
c.
lease contracts
d.
interest payments
29. The payment or receipt of a series of equal cash flows per period, at the end of each period, for a
specified amount of time is called a(n):
a.
annuity due
b.
perpetuity
c.
ordinary annuity
d.
simple interest
30. The difference between an ordinary annuity and an annuity due is:
a.
the interest rate
b.
the timing of the payments
c.
the amount of the payments
d.
the number of periods
31. ____ is the return earned by someone who has forgone current consumption.
a.
The present value
b.
Principle
c.
An annuity
d.
Interest
32. Determine how much $1,000 deposited in a savings account paying 8% (compounded annually) will
be worth after 5 years.
a.
$5,526
b.
$ 784
c.
$1,400
d.
$1,469
33. The earnings of Omega Supply Company have grown from $2.00 per share to $4.00 per share over a
nine year time period. Determine the compound annual growth rate.
a.
11.1%
b.
8%
c.
22.2%
d.
100%
34. Comet Powder Company has purchased a piece of equipment costing $100,000. It is expected to
generate a ten-year stream of benefits amounting to $16,273 per year. Determine the rate of return
Comet expects to earn from this equipment.
a.
16.3%
b.
62.7%
c.
10%
d.
20%
35. Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an
equal amount at the end of each of the next 25 years so that he can retire at age 60. He expects to live
to the maximum age of 80 and wants to be able to withdraw $25,000 per year from the account on his
61st through 80th birthdays. The account is expected to earn 10 percent per annum for the entire
period of time. Determine the size of the annual deposits that must be made by Mr. Moore.
a.
$212,850
b.
$23,449
c.
$2,164
d.
$8,514
36. Determine (to the nearest dollar) the amount you would be willing to pay for a $1,000 par value bond
paying $80 interest each year and maturing in 12 years, assuming you wanted to earn a 9 percent rate
of return.
a.
$929
b.
$573
c.
$1,316
d.
$1,960
37. Determine how much you would be willing to pay for a bond that pays $60 annual interest indefinitely
and never matures (i.e. a perpetuity), assuming you require an 8 percent rate of return on this
investment.
a.
$480
b.
$743
c.
$1,000
d.
$750
38. Air Atlantic (AA) has been offered a 3-year old jet airliner under a 12-year lease arrangement. The
lease requires AA to make annual lease payments of $500,000 at the beginning of each of the next 12
years. Determine the present value of the lease payments if the opportunity cost of funds is 14 percent.
a.
$2,830,000
b.
$13,635,500
c.
$6,000,000
d.
$3,226,200
39. If you invest $10,000 in a 4-year certificate of deposit (CD) paying 10 percent interest compounded
annually, determine how much the CD will be worth at the end of 4 years.
a.
$13,600
b.
$45,730
c.
$14,640
d.
$15,958
40. You sold 100 shares of stock today for $30 per share that you paid $20 for 6 years ago. Determine the
average annual rate of return on your investment, assuming the stock paid no dividends.
a.
25%
b.
8.33%
c.
150%
d.
7%
41. Your grandparents put $1,000 into a savings account for you when you were born 20 years ago. This
account has been earning interest at a compound rate of 7 percent. What is its value today?
a.
$3,870
b.
$1,967
c.
$3,026
d.
$3,583
42. Baggos has seen their EPS increase from $0.30 to $3.16 in seven years. What has been the growth rate
of Baggos’s EPS?
a.
about 30%
b.
about 40%
c.
about 20%
d.
none of these are correct
43. You have just won a $50,000 bond that pays no interest and matures in 20 years. If the discount rate is
10%, what is the present value of your bond?
a.
$7,450
b.
$8,175
c.
$8,900
d.
$1,490
44. BB&C bank has agreed to lend you $30,000 today, but you must repay $42,135 in 3 years. What rate
is the bank charging you?
a.
10%
b.
11%
c.
12%
d.
13%
45. The Florida lottery agrees to pay the winner $250,000 at the end of each year for the next 20 years.
What is the future value of this lottery if you plan to put each payment in an account earning 9
percent?
a.
$2.28 million
b.
$12.79 million
c.
$14.32 million
d.
$5.00 million
46. Billy Bob has decided to put $2,400 a year (at the end of each year) into an IRA over his 40 year
working life and then retire. What will Billy have if the account will earn 10 percent compounded
annually?
a.
$394,786
b.
$ 23,470
c.
$1,062,223
d.
$810,917
47. Jane wants to have $200,000 in an account in 20 years. If her account earns 11 percent per annum over
the accumulation period, how much must she save per year (end of year) to have the $200,000?
a.
$25,116
b.
$3,115
c.
$10,000
d.
$3,492
48. Many IRA funds argue that investors should invest at the beginning of the year rather than at the end.
What is the difference to an investor who invests $2,000 per year at 11 percent over a 30-year period?
a.
$43,785
b.
$36,189
c.
$54,244
d.
There is no difference
49. An insurance company offers you an end of year annuity of $48,000 per year for the next 20 years.
They claim your return on the annuity is 9 percent. What should you be willing to pay today for this
annuity?
a.
$429,600
b.
$438,144
c.
$408,672
d.
none of these are correct
50. New Jersey Mutual has offered you a single premium annuity that will pay you $12,000 per year (end
of year) for the next 15 years. If you must pay $109,296 today for this annuity, what is your expected
rate of return?
a.
8%
b.
9%
c.
7%
d.
10%
51. Columbia Bank & Trust has just given you a $20,000 term loan to pay for a new concrete mixer. The
loan requires five equal annual end of the year payments. If the loan provides the bank with a 12
percent return, what will be your annual payments?
a.
$5,548
b.
$3,148.12
c.
$6,000
d.
$1,666.67
52. Idlewild Bank has granted you a seven year loan for $50,000. If your seven annual end of the year
payments are $11,660.45, what is the rate of interest Idlewild is charging?
a.
14%
b.
23%
c.
12.6%
d.
cannot be determined from the information given
53. Your firm, New Sunrise, has just leased a $28,000 BMW for you. The lease requires six beginning of
the year payments that will fully amortize the cost of the car. What is the amount of the payments if
the interest rate is 12 percent?
a.
$6,810.99
b.
$7,766.99
c.
$6,423.74
d.
$6,081.25
54. The lease on a new office requires an immediate payment of $24,000 plus $24,000 per year at the end
of each of the next 10 years. At a discount rate of 14 percent, what is the present value of this stream
of lease payments?
a.
$130,872
b.
$149,194
c.
$142,710
d.
$264,000
55. Alabama Power has preferred stock that pays an annual dividend of $9.44. If the security has no
maturity, what is it’s value to an investor who wishes to obtain a 9 percent rate of return?
a.
$84.96
b.
$104.89
c.
$95.34
d.
$94.40
56. Designs Now is opening a showcase office to display and sell it’s computer designed poster art.
Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year, $240,000 in
the third year. If Designs uses 11 percent as its discount rate, what is the present value of the cash
flows?
a.
$429,720
b.
$457,620
c.
$456,000
d.
$424,820
57. In six years, your daughter will be going to college. You wish to have a fund that will provide her
$10,000 per year (end of year) for each of her four years in college. How much must you put into that
fund today if the fund will earn 10 percent in each of the 10 years?
a.
$29,744.65
b.
$29,783.76
c.
$17,878.80
d.
$21,651.10
58. What is the future value of a $10,000 college tuition fund if the nominal rate of interest is 12 percent
compounded monthly for five years?
a.
$17,623.42
b.
$18,170
c.
$16,105.10
d.
$16,122.26
59. What is the effective rate of interest on a CD that has a nominal rate of 9.5 percent with interest
compounded monthly?
a.
9.92%
b.
9.74%
c.
10.02%
d.
9.86%
60. John is 25 years old and wishes to retire in 30 years. His plan is to invest in a mutual fund earning a 12
percent annual return and have a $1 million retirement fund at age 55. How much must he invest at the
end of each year to achieve this goal?
a.
$7,499.96
b.
$5,024.60
c.
$4,143.65
d.
$33,333.33
61. Joe Brady just won a $450,000 lottery in Pennsylvania. Instead of receiving a lump sum, he found that
he would receive $22,500 annually (end of year) for 20 years. Joe is 75 years old and wants his money
now. He has been offered $140,827 to sell his ticket. What rate of return is the buyer expecting to
make if Joe accepts the offer?
a.
less than 1%
b.
15%
c.
18%
d.
12%
62. A bank has agreed to loan you $10,000 at 11% for 5 years. You are required to make equal, annual,
end-of-year payments that include both principal and interest on the outstanding balance. Determine
the amount of these annual payments (to the nearest dollar).
a.
$2,000