Ma 162 HW 21: Problem $

Question

A person wants to establish an annuity for retirement. He wants to make monthly deposits for 30 years so that he can then make monthly withdraws of $4,600.00 for 20 years. The annuity earns 7.98% compounded monthly.

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

Value of account at retirement: $

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

Monthly deposit: $

(c) What is the total amount of interest earned during the 50-year period?

Total Interest Earned: $

Answer 1

a: using a present value function in excel, inputting (7.98%/12) for the monthly interest rate, 240 payments (20 years x 12 months per year), and with the annuity completely used in that period, you would need $550,769.06 in the annuity upon retirement.

b. Assuming the same interest rate, and making payments for 360 periods (30 years x 12 months per year), you would need to make monthly payments of $371.06 in order to have your annuity be $550,769.06

c. if you make 360 monthly payments of $371.06, your total payments would be only $133,580.74. thus the total interest earned would simply be the difference between the annuity amount earned and your total payments: interest earned in this case is $417,188.33