Question

A father has saved money in a fund to finance his son’s 4-year university program. The fund pays out 300$ every month at the beginning of each month for 8 months (September through April) plus an extra 2.000$ each September 1st for 4 years. At j4 = 8%, what is the value of the fund on the first day of university, before any withdrawals?

Answer 1

Payout Annuity:

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

where

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

then, the value of the fund on the first day of university:

$P=\frac{300(1-(1+0.08/8)^{-4\cdot8})}{0.08/8}+\frac{2000(1-(1+0.08)^{-4})}{0.08}=8180.88+975.49=9156.37\ \$$