Question

Assume that your father is now 50 years old and plans to retire after 10 years from now. He is expected to live for another 25 years after retirement. He wants a fixed retirement income of Rs. 5,00,000 per annum. His retirement income will begin the day he retires, 10 years from today, and then he will get 24 additional payments annually. Your father has current savings of Rs. 10,00,000 and 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 during each of next 10 years to meet his retirement goal?

Answer 1

Computation of amount required at Retirement:

P = Amount required annually = 500000

n = 25 years

r = return = 10%

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

$= 500000 + \frac{500000 \times (1 - (1+0.1)^{-(25-1)}} {0.1} \\ = 500000 + \frac{500000 \times 0.898474402}{ 0.1} \\ = 500000 + 4492372.01 \\ = 4992372.01$

The amount required at retirement is 4992372.01

Calculation of Annual savings:

n = 10 years

r = annual return = 10%

Let P = Annual Savings required

Amount required at retirement = 4992372.01

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

$\frac{P \times ((1+0.1)^{10} - 1) }{0.1} + (1000000 \times (1+0.1)^{10}) = 4992372.01 \\ \frac{P \times 1.59374246}{0.1} + (1000000 \times 2.59374246) = 4992372.01 \\ P \times 15.9374246 = 2398629.55 \\ P = 150502.9583$

Therefore, amount required to save each year is 150502.96