Question

You put aside $100,000 in year t = 0, and let it grow at 6.3% interest for 5 years. Exactly one year after that you start to withdraw your money for 3 years in equal amounts until it is exhausted. How much can you withdraw per year? Answer to the nearest cent, xxx.xx and enter without a dollar sign.

Answer 1

Investment amount in year t = 0 = P = $100,000

r = interesr rate = 6.3%

n = 5 years

Amount of Money at the time t = 5 = P * (1+r)^n

= $100,000 * (1+6.3%)^5

= $100,000 * 1.35727023

= $135,727.023

Calculation of Amount of Annual Withdrawl

Value of Investment = PV = $135,727.02

n = 3 years

r = 6.3%

Annual Withdrawl = [r*PV] / [1 - (1+r)^-n]

= [6.3% * $135,727.02] / [1 - (1+6.3%)^-3]

= $8,550.80245 / 0.167469398

= $51,058.8952

Therefore, Withdrawl per year for 3 years is $51,058.90