Question

You begin saving for your retirement through an ordinary annuity that is deposited into a mutual fund over the next 30 years (30 payments in total). Assume you leave your funds in this mutual fund throughout your lifetime and it earns 12% per year. Once you retire you expect to live for an additional 25 years. In retirement you would like to receive an annuity due for these 25 years of $200,000 per year.

How much must you deposit into this mutual fund annually in order to receive the retirement benefit you desire? Assume your money is left in the mutual fund earning 12% per year.

Answer 1

Retirement fund required is:

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	200,000.00
r=	Rate of interest per period
	Annual interest	12.00%
	Number of payments per year	1
	Interest rate per period	0.12/1=
	Interest rate per period	12.000%
n=	number of periods:
	Number of years	25
	Periods per year	1
	number of payments	25
	Present value of annuity=	200000* [ (1- (1+0.12)^-25)/0.12 ]
	Present value of annuity=	1,568,627.82

Annual payment to achieve fund value in 30 years is:

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	1,568,627.82
Rate per period	r
Annual interest		12.0%
Number of payments per year		1
Interest rate per period		0.12/1=
Interest rate per period		12.000%
Number of periods	n
Number of years		30
Periods per year		1
number of periods		30
Period payment	=	1568627.82*0.12/ [(1+0.12)^30 -1]
	=	6,499.86

Annual payment is $6,499.86

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