Answer to Question #123557 in Finance for yash moryani

Question

Neha would retire 30 years from today and she would need ₹ 6,00,000 per year after her retirement, with the first retirement funds withdrawn one year from the day she retires.
Assume a return of 7% per annum on her retirement funds and if her planning is for 25 years after retirement, Calculate:
a. How much lumpsum she should deposit in her account today so that she has enough funds for retirement?
b. How much she should deposit each year so that she has enough funds for retirement?

Answer 1

a) Cash PV annuity factor

$= (1 – (\frac{\frac{1}{(1+0.07)^{25}}}{0.07})= (1 – (\frac{\frac{1}{5.427}}{0.07})= \frac{(1 – 0.1842)}{0.07}=\frac{0.81574}{0.07}=11.6535832$

PV (annuity) with payment of Rs.

$600000 = 600000\times11.6535832= 6 992 149.92$

PV today

$\frac{6 992 149.92}{(1+0.07)^{30}}=918 538.58$

b) FV annuity factor

$\frac{ ((1+r)^n- 1)}{r}= \frac{((1+0.07)^{30}- 1)}{0.07}=\frac{((1.07)^{30}- 1)}{0.07}= \frac{(7.6122-1)}{0.07}= \frac{6.6122}{0.07}= 94.46$

A = PV (annuity)/ FV annuity factor

$= \frac{6 992 149.92}{94.46}= 74022.34$