Finance question related to retirement

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 savings @ 10% p.a., annually compounding. How much (to the

nearest of rupee) must your father save today to meet his retirement goal?

Answer 1

Because the first retirement payment is made on the day he retires, this is an annuity due.

He will receive:

Rs. 1,00,000 per year

15 total payments

10% annual return

First, find the amount needed at retirement (5 years from today).

Present value of an ordinary annuity:

PV = 100,000[(1 - 1/1.10^15) / 0.10]

PV = Rs. 760,608

Because the first payment occurs immediately at retirement, multiply by 1.10:

PV at retirement = 760,608(1.10)

= Rs. 836,669

Now discount this amount back 5 years to today:

PV today = 836,669 / 1.10^5

PV today = Rs. 519,505

Therefore, your father must save approximately:

Rs. 5,19,505 today.