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:

$P+\frac{P(1-(1+r)^{-n-1})}{r}=100000+\frac{100000(1-(1+0.1)^{-15-1})}{0.1}=836668.75$

Calculation of Annual savings:

n = 5 years

r = annual return = 10%

Let p is Annual Savings required, then:

$p((1+r)^n-1)/r=836668.75$

$p((1+0.1)^5-1)/0.1=836668.75$

$0.61051p=83668.75$

$p=137047.30$