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41. If the future value of an annuity due is $25,000 and $24,000 is the future value of an
ordinary annuity that is otherwise similar to the annuity due, what is the implied discount rate?
42. A furniture store is offering free credit on purchases over $1,000. You observe that a big-
screen television can be purchased for nothing down and $4,000 due in one year. The store next
door offers an identical television for $3,650 but does not offer credit terms. Which statement
below best describes the cost of the "free" credit?
43. How much must be invested today in order to generate a 5-year annuity of $1,000 per
year, with the first payment 1 year from today, at an interest rate of 12%?
44. The salesperson offers, "Buy this new car for $25,000 cash or, with an appropriate down
payment, pay $500 per month for 48 months at 8% interest." Assuming that the salesperson does
not offer a free lunch, calculate the "appropriate" down payment.
45. What is the present value of the following payment stream, discounted at 8% annually:
$1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3?
46. You invested $1,200 three years ago. During the three years, you earned annual rates of
return of 4.8%, 9.2%, and 11.6%. What is the value of this investment today?
47. You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end
of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an
interest rate of 7%?
48. A cash-strapped young professional offers to buy your car with four, equal annual
payments of $3,000, beginning 2 years from today. Assuming you're indifferent to cash versus
credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you
accept?
49. How much more is a perpetuity of $1,000 worth than an annuity of the same amount for
20 years? Assume an interest rate of 10% and cash flows at the end of each period.
50. A stream of equal cash payments lasting forever is termed:
51. Which one of the following factors is fixed and thus cannot change for a specific
perpetuity?
52. The present value of a perpetuity can be determined by:
53. A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What
is its present value?
54. A corporation has promised to pay $1,000 20 years from today for each bond sold now.
No interest will be paid on the bonds during the 20 years, and the bonds are discounted at an
interest rate of 7%, compounded semiannually. Approximately how much should an investor pay
for each bond?
55. Your car loan requires payments of $200 per month for the first year and payments of
$400 per month during the second year. The annual interest rate is 12% and payments begin in
one month. What is the present value of this 2-year loan?
56. Which one of the following will increase the present value of an annuity, other things
equal?
57. What is the present value of a five-period annuity of $3,000 if the interest rate per period
is 12% and the first payment is made today?
58. Three thousand dollars is deposited into an account paying 10% annually to provide three
annual withdrawals of $1,206.34 beginning in one year. How much remains in the account after
the second payment has been withdrawn?
59. How many monthly payments remain to be paid on an 8% mortgage with a 30-year
amortization and monthly payments of $733.76, when the balance reaches one-half of the
$100,000 mortgage?
60. What is the present value of a four-year annuity of $100 per year that begins 2 years from
today if the discount rate is 9%?
61. If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years
with monthly payments of $965.55, how much interest is paid over the life of the loan?
62. $50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest.
Approximately how much principal is amortized with the first payment?
63. An amortizing loan is one in which:
64. You're ready to make the last of four equal, annual payments on a $1,000 loan with a 10%
interest rate. If the amount of the payment is $315.47, how much of that payment is accrued
interest?
