Question

You are planning to save for retirement over the next 30 years. To do this, you will invest $700 a month in a stock account and $400 a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with a 9 percent return. Required: How much can you withdraw each month from your account assuming a 20-year withdrawal period?(Do not round your intermediate calculations.) rev: 09_17_2012 $214,222.69 $18,208.93 $17,851.89 $711,295.81 $17,494.85

Answer 1

$17,851.89

Step-1:Calculation of future value of investment
# 1
Future value of stock investment		=	Monthly investment * Future value of annuity of 1
		=	$                   700	*	2260.487925
		=	$ 15,82,341.55
Working:
Future value of annuity of 1		=	(((1+i)^n)-1)/i			Where,
		=	(((1+0.008333)^360)-1)/0.008333			i	10%/12	=	0.008333
		=	2260.487925			n	30*12	=	360
# 2
Future value of bonds investment		=	Monthly investment * Future value of annuity of 1
		=	$                   400	*	1004.515042
		=	$    4,01,806.02
Working:
Future value of annuity of 1		=	(((1+i)^n)-1)/i			Where,
		=	(((1+0.005)^360)-1)/0.005			i	6%/12	=	0.005
		=	1004.515042			n	30*12	=	360
# 3
Future value of investment in 25 years		=	Future value of stock investment + Future value of bond investment
		=	$ 15,82,341.55	+	$ 4,01,806.02
		=	$ 19,84,147.56
Step-2:Calculation of monthly withdrawal
Monthly withdrawal		=	Present value / Present value of annuity of 1
		=	$ 19,84,147.56	/	111.144954
		=	$       17,851.89
Working:
Present value of annuity of 1		=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.0075)^-240)/0.0075		i	9%/12	=	0.0075
		=	111.144954		n	20*12	=	240