Question

A person wants to establish an annuity for retirement. He wants to make quarterly deposits for 25 years so that he can then make quarterly withdraws of $14,500.00 for 15 years. The annuity earns 6.94% 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 25 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 40-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

a)

C = Cash flow per period

i = interest rate

n = number of payments

PV= 14,500*((1-(1+ 6.94/400)^(-15*4))/(6.94/400))

PV= 537989.40

b)

C = Cash flow per period

i = interest rate

n = number of payments

537989.40 = Cash Flow*(((1+ 6.94/400)^(25*4)-1)/(6.94/400))

Cash Flow = 2035.70

c)

Total interest = amount after 25 years - (quarterly deposit*years deposited*quarters per year) + (quarterly withdrawal*years withdrawn*quarters per year)-amount after 25 years

=537989.40-2035.70*25*4+14,500*4*15-537989.40 =666430