Question

Question #1: You are planning to save for retirement over the next 35 years. To do this, you will invest $900 per month in a stock account and $500 per month in a bond account. The return of the stock account is expected to be 11 percent, and the bond account will pay 7 percent. When you retire, you will combine your money into an account with a 8 percent return.

How much can you withdraw each month from your account assuming a 30-year withdrawal period? _____

Answer 1

Monthly withdrawal is $ 39,157.92

Step-1:Future value of stock investment
Future value	=	Monthly Investment	*	Future value of annuity of 1
	=	$             900.00	*	4928.816015
	=	$ 44,35,934.41
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.009167)^420)-1)/0.009167		i	=	11%/12	=	0.009167
	=	4928.816015		n	=	35*12	=	420
Step-2:Future value of bond investment
Future value	=	Monthly Investment	*	Future value of annuity of 1
	=	$             500.00	*	1800.882982
	=	$    9,00,441.49
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.005833)^420)-1)/0.005833		i	=	7%/12	=	0.005833
	=	1800.882982		n	=	35*12	=	420
Step-3:Monthly Withdrawal
Monthly Withdrawal	=	Total investment amount	/	Present value of annuity of 1
	=	$ 53,36,375.90	/	136.2783152
	=	$ 39,157.92
Working:
Total investment amount	=	Future value of stock investment	+	Future value of bond investment
	=	$ 44,35,934.41	+	$ 9,00,441.49
	=	$ 53,36,375.90
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.006667)^-360)/0.006667		i	=	8%/12	=	0.006667
	=	136.2783152		n	=	30*12	=	360