Question

1 point) A person wants to establish an annuity for retirement. He wants to make quarterly deposits for 30 years so that he can then make quarterly withdraws of $15,000.00 for 15 years. The annuity earns 7.48% compounded quarterly.

(a) How much will have to be in the account at the time he retires?

Value of account at retirement:

[Note: Your answer is a dollar amount and should have a dollar sign and exactly two decimal places.]

(b) How much should be deposited each quarter for 30 years in order to accumulate the required amount?

quarterly deposit:

[Note: Your answer is a dollar amount and should have a dollar sign and exactly two decimal places.]

(c) What is the total amount of interest earned during the 45-year period?

Total Interest Earned:

[Note: Your answer is a dollar amount and should have a dollar sign and exactly two decimal places.]

Answer 1

i = 7.48% compounded quarterly = 7.48% / 4 = 1.87% per quarter

deposit quarters = 30 * 4 = 120

Withdrawl quarters = 15*4 = 60

Withdrawl amount = 15000

a) Value of account at time of retirement = 15000*(P/A,1.87%, 60) = 15000 * 35.88131 = 538219.65

b) Deposit to made every quarter = 538219.65 * (A/F, 1.87%,120) = 538219.65 * 0.002270 = 1221.76

c) interest earned = 538219.65 - 1221.76 * 120 = 538219.65 - 146611.0327 = 391608.62