Question

Your older brother turned 35 today, and he is planning to save $15,000 per year for retirement, with the first deposit to be made one year from today. He will invest in a mutual fund that's expected to provide a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year.

Answer 1

Step 1:	Calculation of value of saving at age 65
	Future Value of an Ordinary Annuity
	= C*[(1+i)^n-1]/i
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	= $15000[ (1+0.075)^30 -1] /0.075
	= $15000[ (1.075)^30 -1] /0.075
	= $15000[ (8.755 -1] /0.075]
	= $1,550,991.04
Step 2:	Calculation of amount that can be withdraw each year
	Present Value Of An Annuity
	= C*[1-(1+i)^-n]/i]
	Where,
	C= Cash Flow per period
	i = interest rate per period
	n=number of period
	1550991.04= C[ 1-(1+0.075)^-25 /0.075]
	1550991.04= C[ 1-(1.075)^-25 /0.075]
	1550991.04= C[ (0.836) ] /0.075
	C= 139140.45
	Annual Withdrawal = $139140.45