Question

Assume that your father is now 55 years old and plans to retire after 5 years from now. He is expected to live for another 15 years after retirement. He wants a fixed retirement income of Rs. 1,00,000 per annum. His retirement income will begin the day he retires,

5 years from today, and then he will get 14 additional payments annually. He expects to earn a return on his savings @ 10% p.a., annually compounding. How much (to the nearest of rupee) must your father save today to meet his retirement goal?

Answer 1

P = Amount required annually = 100000

n = 15 years

r = return = 10%

Amount required at retirement $= P + \frac{P \times (1 - (1+r)^{-(n-1)}) }{ r}$

$= 100000 + \frac{100000 \times (1 - (1+0.1)^{-(15-1)}} {0.1} \\ = 100000 + \frac{100000 \times 0.736687545}{ 0.1} \\ = 100000 + 736668.7457 =836668.7457$

The amount required at retirement is =836668.7457

Calculation of Annual savings:

n = 5 years

r = annual return = 10%

Let P = Annual Savings required$P×\frac{(1+r)^n-1}{r}$

​836668.7457=$P×\frac{(1+0.1)^5-1}{0.1}$

$0.61051P=83668.7457$

$P=\frac{83668.7457}{0.61051}$

$P=137047.2977$