Question 1:
Present value of an annuity. For each of the cases shown in the following table, calculate the present value of the annuity, assuming that the annuity cash flows occur at the end of each year.
|
Case
|
Amount of Annuity
|
Interest rate
|
Period (years)
|
|
A
|
$12,000
|
7%
|
3
|
|
B
|
55,000
|
12
|
15
|
|
C
|
700
|
20
|
9
|
|
D
|
140,000
|
5
|
7
|
|
E
|
22,500
|
10
|
5
|
Question 2:
Creating a retirement fund. To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $2,200,000 by that time. You plan to make equal annual end-of-year investments into an account providing and 8 percent annual rate of return.
a. How much must the annual investments be to create the $2,200,000 fund by the end of 42 years?
b. If you can earn a 10 percent return, rather than an 8 percent return, does this have a significant impact on the yearly amount you must invest? What is the amount you must invest? Explain what has happened.
c. If you can only afford to invest $4,000 per year and will receive a 9 percent return, how much will you have in 42 years' time?
d. If you can invest $5,000 per year and still want to have $2,200,000 in 42 years' time, what rate of return must you earn on the investments?