Question

Suppose you want to have $500,000 for retirement in 35 years. Your account earns 4.3% interest. How much would you need to deposit in the account each month?
Round your answer to the nearest cent as needed.
$

How much would you need to deposit in an account each month in order to have $20,000 in the account in 9 years? Assume the account earns 2.6% interest.

You have $500,000 saved for retirement. Your account earns 6.4% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?

Answer 1

1.The formula for computing the future value (A) of annuity is A = P[(1+r)ⁿ -1]/r where P is periodic payment, r is the interest rate per period, and n is the number of periods. Here, A = 500000, r = 4.3/1200 = 43/12000 and n = 35*12 = 420. Hence, 500000 = P[ (1+43/12000)⁴²⁰-1]/(43/12000) so that P = [500000*(43/12000)]/3.492053579 = $ 513.07( on rounding off to the nearest cent).

2. Here, A = $ 20000, r = 2.6/1200 = 13/6000, and n = 9*12 = 108. Hence, 20000 = P[(1+13/6000)¹⁰⁸-1]/ (13/6000) so that P = [20000*(13/6000)]/0.263324661 = $ 164.56( on rounding off to the nearest cent).

3. The formula for computing monthly withdrawals (P) is P = r(PV)/[1-(1+r)^-n] where PV is the present value and r, n are as in 1. above. Here, PV = 50000, r = 6.4/1200 = 16/3000 and n = 20*12 = 360. Hence, P = (16/3000)*500000/[1-(1+16/3000)^-360] = (8000/3)/(1-0.147356843) = 8000/2.557929471 = $ 3127.53( on rounding off to the nearest cent).