Question

Monica has decided that she wants to build enough retirement wealth that, if invested at 10 percent per year, will provide her with $5,500 of monthly income for 25 years. To date, she has saved nothing, but she still has 30 years until she retires. How much money does she need to contribute per month to reach her goal

Answer 1

Amount required on retirement date to get 5500 per month for 25 years is:

	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	5,500
r=	Rate of interest per period
	Annual interest	10.00%
	Number of interest payments per year	12
	Interest rate per period	0.1/12=
	Interest rate per period	0.83%
n=	number of periods:
	Number of years	25
	Periods per year	12
	number of periods	300
	Present value of annuity=	5500* [ (1- (1+0.00833)^-300)/0.00833 ]
	Present value of annuity=	6,05,259.77

To have 605259.77 on retirement fund, monthly contribution required is:

Payment required	=		FV*r /[(1+r)^n -1]
Future value	FV		6,05,259.77
Rate per period	r
Annual interest			10%
Number of interest payments per year			12
Interest rate per period			0.1/12=
Interest rate per period			0.833%
Number of periods	n
Number of years			30
Periods per year			12
number of periods			360
Monthly payment	=		605259.77*0.008333/ [(1+0.008333)^360 -1]
	=		267.76