Answer to Question #192978 in Management for preksha

Question

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

​836668.7457=p*(1+0.1)⁵-1/0.1

$0.61051p=83668.7457$

$P=137047.2977$