Question

You are 40 years old today and want to plan for retirement at age 65. You want to set aside an equal amount every year from now to retirement. You expect to live to age 95 and want to withdraw a fixed amount each year during retirement that at age 65 will have the same purchasing power as $70,000 has today. You plan on withdrawing the money starting the day you retire. You have $15,000 saved for retirement today. Inflation is assumed to be 3.0% in the future. You expect to earn an 8% return on your investments in the future. How much do you need to save each year until retirement to meet your goal?

	A.	$23,975.04
	B.	$21,164.68
	C.	$21,011.18
	D.	$22,970.27

Answer 1

You want to have a fixed amount each year during retirement but the amount to withdraw during retirement is $70,000 in today's dollar terms which is subject to inflation till the retirement withdrawal happens.

Withdrawal will strat from age 65.

Retirment amount after inflation = Value Today*(1+Inflation)^25

=$70,000*(1+0.03)^25

=$146,564.46

Now, calculating the Prsent value of the retirment withdrwal:-

Where, C= Periodic Withdrawal =$146,564.46

r = Periodic Interest rate = 0.08

n= no of periods = 30

Present Value = $1781,990.21

- You have saved $15,000 for retirement at age 40. Now, we will use the above Present value as future value to compute the amount need to be saved each year to accumulate the Retirement fund using the formula:-

Where, C= Periodic Payments

r = Periodic Interest rate = 0.08

n= no of periods = 25

Invested Amount = $15,000

Future Value = $1781,990.21

C = $ 22,970.27

So, amount you need to save each year until retirement to meet your goal is $ 22,970.27

hence, Option D

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