Question

Beginning at age 30, Ms. Trinh invests $2,000 each year into an IRA account until she retires. When she retires, she plans to withdraw equal amounts each year that will deplete the account when she is 90. Find the annual amount she will receive if she retires at age 70 and the account pays 6% compounded annually.

Answer 1

Value of her deposits is:

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                2,000.00
rate of interest per period	r=
Rate of interest per year		6.0000%
Payment frequency		Once in 12 months
Number of payments in a year		1.00
rate of interest per period		0.06*12/12	6.0000%
Number of periods
Number of years		40
Number of payments in a year		1
Total number of periods	n=	40
FV of annuity	=	2000* [ (1+0.06)^40 -1]/0.06
FV of annuity	=	309,523.93

her investment nest egg is $309,523.93

Her withdrawal will be:

	Annuity payment=	P/ [ [1- (1+r)-n ]/r ]
P=	Present value	309,523.93
r=	Rate of interest per period
	Rate of interest per annum	6.0%
	Payments per year	1.00
	Rate of interest per period	6.000%
n=	number of payments:
	Number of years	20
	Payments per year	1.00
	number of payments	20
	Annuity payment=	309523.93/ [ (1- (1+0.06)^-20)/0.06 ]
	Annuity payment=	26,985.71

Her annual receipt is $26,985.71

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