Question

Your sister turned 35 today, and she is planning to save $40,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

	a.	$363,620.37
	b.	$389,593.25
	c.	$452,670.26
	d.	$371,041.19
	e.	$359,909.96

Answer 1

Given,

Annual saving (A) = $40000

Years before retirement (n) = 30 years

Rate of return (r) = 7.5% or 0.075

Retirement period (n₁) = 25 years

Solution :-

Value at the time of retirement = A/r x [(1 + r)ⁿ - 1]

= $40000/0.075 x [(1 + 0.075)³⁰ - 1]

= $40000/0.075 x [(1.075)³⁰ - 1]

= $40000/0.075 x [8.75495519 - 1]

= $40000/0.075 x 7.75495519 = $4135976.10

Annual withdrawal = [Value at the time of retirement x r] [1 - (1 + r)^-n₁]

= [$4135976.10 x 0.075] [1 - (1 + 0.075)^-25]

= $310198.2075 [1 - (1.075)^-25]

= $310198.2075 [1 - 0.16397906]

= $310198.2075 0.83602094 = $371041.19

option 'd' is correct.