Question

On his 25th birthday Yves deposited 2.500$ in a fund paying j1 = 10% and continued to make such deposits each year, the last on his 49th birthday. Beginning on his 50th birth- day, Yves plans to make equal annual withdrawals of 35.000$. How many withdrawals can be made? What additional sum paid with the last withdrawal will exhaust the fund? What sum paid one year after the last full withdrawal will exhaust the fund?

Answer 1

Apply the Annuity Formula

$FV=A\frac{(1+i)^n-1}{i}$

A=2500

i=0.1

n=25

$FV=A\frac{(1+i)^n-1}{i}=2500\frac{(1+0.1)^{25}-1}{0.1}=245867.65$

$\frac{245867.65}{35000}=7.025$

7 withdrawals can be made

$245867.65-35000\times7=868.65$ additional sum paid with the last withdrawal will exhaust the fund

$FV=A\frac{(1+i)^n-1}{i}=868.65\frac{(1+0.1)^{1}-1}{0.1}=868.25$

sum paid one year after the last full withdrawal will exhaust the fund