Question

You plan to retire in year 20
Your retirement will last 25 years starting in year 21
You want to have $50,000 each year of your retirement.
How much would you have to invest each year, starting in one year, for 15 years , to exactly pay for your retirement ,if your investments earn 6.00% APR (compounded annually)?

Answer 1

Step-1:Present value of retirement cash flow in year 20
Present value	=	Annual cash flow	*	Present value of annuity of 1
	=	$     50,000.00	*	12.78336
	=	$ 6,39,167.81
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.06)^-25)/0.06		i	6%
	=	12.78335616		n	25
Step-2:Investment each year
Each year investment	=	Value of investment in year 20	/	Future value of 1 in year 20
	=	$ 6,39,167.81	/	31.1485
	=	$     20,520.02
Working:
Future value of 1 in year 20	=	((((1+i)^n1)-1)/i)*(1+i)^n2			Where,
	=	((((1+0.06)^15)-1)/0.06)*(1+0.06)^5			i	6%
	=	31.14849824			n1	15
					n2	5