Question

A 22-year old engineering graduate wants to accumulate $2,500,000 to be available when she retires 40 years from today. She investigates several investment options and she decides to invest in a stock market index fund after discovering that the long-term average return for the stock market is 12.8% per year. Since this will be a tax-sheltered account, she plans to ignore the impact of taxes.

If she plans to make the first deposit 1 year from today and each annual payment will be $200 greater than the previous year’s payment,

(i) What is the dollar amount of the first deposit?

(ii) What is the dollar amount of the last deposit?

Please Show Work.

Answer 1

F = 2500000

t = 40 years

i = 12.8%

increase in amount each year = 200

Let First deposit be A1

Present value of the future value = 2500000 * (P/F, 12.8%,40)

= 2500000 * 0.00808418

= 20210.452

Present value of deposit = A1 *(P/A, 12.8%, 40) + 200 * (P/G, 12.8%, 40)

= A1 *7.74934 + 200 * 58.01543

= A1 *7.74934 + 11603.086

This should be equal to the preesnt value calculated above

A1 *7.74934 + 11603.086 = 20210.452

A1 = (20210.452 - 11603.086) / 7.74934

A1 = 1110.72

First deposit = 1111 (rounding off)

Last deposit = 1111 + 200 *39 = 1111 + 7800 = 8911