Answer to Question #174465 in Financial Math for Kaushik

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 saving @ 10% p.a. annually compounding. How much must your father save today for 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*((1+r)ⁿ-1)/r

​836668.7457=p*(1+0.1)⁵-1/0.1

$0.61051p=83668.7457$

$P=137047.2977$