Question

7)	You just turned 50 years old and are planning to retire in 15 years.
	You have decided you would like to receive an annuity rather
	than keeping a lum sum. If you invest $12,500 at the end of
	each of the next 10 years, what will your annual payment
	be at the beginning of the first year of your retirement?
	You can assume an interest rate of 6.5% for the entire period.
	The value of $12,500 deposited annually in a fund will amount to the following in fifteen years:
		FV =	12,500{[(1+.065)10-1]/.065} = $302,277.12
		FV =	$302,277.12
	The annuities per year over the next fifteen years at 6.5% will be:
		$302,277.12 = X{[1-(1/(1+.065)15)]/.065}
		Solving for X, annual cash flows, X = $27,433.58
		PMT =

Answer 1

Total cumulative Value of saving at end of year 10 is calculated in excel and screen shot provided below:

Cumulative value of saving at end of year 10 is $168,680.28.

after 10 year 5 year more remains for retirement. so for next five year amount will grow at 6.50%.

So total value at time of retirement = $168,680.28 × (1 + 6.50%) ^ 5

= $168,680.28 × 1.3700

= $231,106.60.

total value at time of retirement will be $231,106.60.

annual amount he can withdraw fro next 15 year after retirement is calculated in excel and screen shot provided below:

He can withdraw $24,578.83 each year.