Question

Aldous wants to withdraw 50000 every 4 months for 15 years. How much must Aldous deposit at rate 12% per year compounded quarterly for the annuity?

Answer 1

Payout Annuity:

$P=\frac{d(1-(1+r/k)^{-nk})}{r/k}$

where

P is the balance in the account at the beginning (starting amount, or principal)

d is the regular withdrawal (the amount you take out each year, each month, etc.)

r is the annual interest rate

k is the number of compounding periods in one year

N is the number of years we plan to take withdrawals

$P=\frac{50000(1-(1+0.12/3)^{-15\cdot3})}{0.12/3}=1036001.99$