Question

A man is planning to retire in 20 years. He wishes to deposit a regular amount every three months until he retires, so that, beginning one year following his retirement, he will receive annual payments of $60,000 for the next 15 years. How much must he deposits if the annual interest rate is 6% compounded quarterly? (Note that the last deposit is made on the date of the end of 20th year, and first withdrawal is at the end of 21st year.)

Answer 1

Let the quarterly deposit be X. We have 80 quarters from now to 20 years. For next 4 quarters, the amount accumulated is added with interest. The amount accumulated after 21 years is then depleted at a rate of 60000 per year for next 15 years. Quarterly rate is 1.5% and Annual rate effective is (1 + 6%/4)^4 - 1 = 6.3636%

X(F/A, 1.5%, 80)(F/P, 1.5%, 4) = 60000(P/A, 6.3636%, 15)

X*152.710852*1.0614 = 60000*9.626301

X = 60000*9.626301/152.710852*1.0614

= 3563.50