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

it's an annuity

find the future value of annite:

$FV=A\frac{(1+r)^n-1}{r}=15000\frac{(1+0.01)^{240}-1}{0.01}=14 838 830.6$

find the current value of annite:

$PVA=PMT\frac{1-\frac{1}{(1+r)^n}}{r}=45000\frac{1-\frac{1}{(1+0.01)^{240}}}{0.01}=4 086 873 .73$

14 838 830.6-4 086 873.73=10 751 956.9