Answer to Question #176135 in Finance for Sandeep

Question #176135

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?


1
Expert's answer
2021-04-06T05:40:15-0400

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} \\\\\n\n= 100000 + \\frac{100000 \\times 0.736687545}{ 0.1} \\\\\n\n= 100000 + 736668.7457\n\n=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\u00d7\\frac{(1+r)^n-1}{r}"

​836668.7457="P\u00d7\\frac{(1+0.1)^5-1}{0.1}"

"0.61051P=83668.7457"

"P=\\frac{83668.7457}{0.61051}"

"P=137047.2977"

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