Answer to Question #227238 in Financial Math for Dudu

Question

Question 2 Upon their retirement in a meeting with their advisor, mr and mrs Moraba determined the amount that they will need in order to live comfortably. They expect a 20-year retirement period. How much should mr and mrs Moraba deposit now in a bank account paying 7,5% interest per year, compounded yearly to be able to withdraw the amount of R480700 at the end of each year, starting one year from now?

Answer 1

$n=20{years}$

$r=7.5\%$

$A=R480700$ (amount to be withdrawn yearly)

$PV=$ amount deposited presently

$\therefore$ $PV=A[\frac{1-{(1+r)^{-n}}}{r}]$

$PV=R480700[\frac{1-{(1+0.075)^{-20}}}{0.075}]$

$PV=R4900491.996$

Mr and Mrs Moraba hould deposit R4900491.996 now to be able to withdraw R480700 yearly.