Question

You will deposit $80 at the end of each month for 15 years into an account with annual interest rate 3% compounded monthly, and then withdraw equal amounts at the end of each month for the following 25 years, ending with a zero balance. What will your monthly withdrawals be?

Answer 1

Fund balance at the end of 15 years is:

FV of annuity	=	P * [ (1+r)^n -1 ]/ r
Periodic payment	P=	$                    80.00
rate of interest per period	r=
Rate of interest per year		3.0000%
Payment frequency		Once in 1 months
Number of payments in a year		12.00
rate of interest per period		0.03*1/12	0.2500%
Number of periods
Number of years		15
Number of payments in a year		12
Total number of periods	n=	180
FV of annuity	=	80* [ (1+0.0025)^180 -1]/0.0025
FV of annuity	=	18,157.82

Amount of withdrawal each month for 25 years will be:

	Annuity payment=	P/ [ [1- (1+r)-n ]/r ]
P=	Present value	18,157.82
r=	Rate of interest per period
	Rate of interest per annum	3.0%
	Payments per year	12.00
	Rate of interest per period	0.250%
n=	number of payments:
	Number of years	25
	Payments per year	12.00
	number of payments	300
	Annuity payment=	18157.82/ [ (1- (1+0.0025)^-300)/0.0025 ]
	Annuity payment=	86.11

Amount of withdrawal will be $86.11

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