Question

Assume that you have 40 years until retirement and have just started your first job. Once you retire, you anticipate that you will live for 30 additional years. Assume that you will require $100,000 per year to support yourself in retirement. All investments that you make will go into and stay an account that returns 7.8% per year (however much you have at retirement will sit that account and continue to accrue interest on the remaining balance. How much will you have to save each year over the next years to meet your goal? Assume that your first investment occurs at the end of your first year of work 1) and that the last of your 40 investments occurs on the last day that you are employed yr 40)For simplicity, assume that your first withdrawal at the end of your first retirement year (yr 41)

Answer 1

Fund balance required by the time of retirement is:

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	100,000.00
r=	Rate of interest per period
	Annual interest	7.80%
	Number of payments per year	1
	Interest rate per period	0.078/1=
	Interest rate per period	7.800%
n=	number of periods:
	Number of years	30
	Periods per year	1
	number of payments	30
	Present value of annuity=	100000* [ (1- (1+0.078)^-30)/0.078 ]
	Present value of annuity=	1,147,359.04

Annual payment required to achieve fund value in 40 years is:

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	1,147,359.04
Rate per period	r
Annual interest		7.8%
Number of payments per year		1
Interest rate per period		0.078/1=
Interest rate per period		7.800%
Number of periods	n
Number of years		40
Periods per year		1
number of periods		40
Period payment	=	1147359.04*0.078/ [(1+0.078)^40 -1]
	=	4,667.94

Annual payment required is $4,667.94

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