Answer to Question #148968 in Finance for Aanchal

Question

Mrs. Ram has been saving Rs.15,000 per month for the last 5 years and continue to save the same amount for the next 15 years for her retirement at age 60. The return on investment is 12% p.a. compounded monthly. If she withdraws Rs.45,000 per month after retirement (after 15 years) for the next 20 years (i.e. from age 60 to 80), how much money will she have at age 80? Assume the same rate of interest on post retirement investment

and withdrawal is at the beginning of the month.

Answer 1

annuity savings:

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

$r=\frac{0,12}{12}=0.01$

$n=20\times12=240$

$FV=15 000\times\frac{(1+0.01)^{240}-1}{0.01}=14 838 830.48$

an annuity payment is made at the beginning of each period, the so-called prenumerando annuity, the formula for calculating its present value is as follows

$PVA=A\times\frac{1-(1+r)^{-n}}{r}\times(1+r)=45 000\times\frac{1-(1+0.01)^{-240}}{0.01}\times(1+0,01)=4 127 742.47$

$14 838 830.48-4 127 742.47=10 711 088.01$