Answer to Question #145286 in Financial Math for mayuri

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 must your mther save durhlg each of next 10 years to meet his retirenent goal?

Answer 1

P = Amount required annually/per annum = Rs 500,000

n = 25 years

r = return = 10%

We can now obtain the Amount needed retirement, thus $=P + \frac{P \times [1 - (1+r)^{-(n-1)}] }{ r}$

$= Rs 500,000 + \frac{Rs 500,000 \times [1 - (1+10\%)^{-(25-1)}]}{10\%}$

$= Rs 500,000 +\frac{ Rs 500,000 \times 0.898474402 }{ 0.1}$

= Rs 500,000 + Rs 4,492,372.01

= Rs 4,992,372.01

The Total amount needed at retirement =Rs 4,992,372.01

 

Consider here also;

n = 10 years

r = annual return = 10%

Take P = Annual Savings needed

Therefore, the Amount needed at retirement = Rs 4,992,372.01

 

We can use this to get the amount required to save per annum as follows.

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

We then substitute;$[P\times\frac{ [(1+10)^9] }{ 10\%}] + [Rs 1,000,000 \times (1+10)^{10}] = Rs 4,992,372.01$

$[P \times [\frac{(1+10\%)^9 }{10}] + [Rs 1,000,000 \times (1+10)^{10}] = Rs 4,992,372.01$

$P \times 15.9374246 = Rs 2,398,629.55$

this implies that, $P = Rs 150,502.9583$

Hence, the amount require to save per annum $= Rs 150,502.96$