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Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. He would now like to draw a monthly salary from the account. Determine the amount that Stan can withdraw each month for 20 years, if he plans on not having anything in the account at the end of the 20 year period and no future deposits are made to the account.

Respuesta :

mathmate
The future value of a monthly deposit A=125.30 at annual interest i=0.015 per annum for n=35 years compounded monthly is given by
FV=A((1+i/12)^(12*n)-1)/(i/12)
=125.30(1+0.015/12)^(12*35)/(0.015/12)
=$69156.05

The annuity formula is given by
Payment = r(PV)/(1-(1+r)^(-n))
where
r=interest rate per period = 0.015/12
PV= $69156.05
n=20*12=240
so
Payment = (0.015/12)69156.05/(1-(1+0.015/12)^(-240))
= $333.71  per month.
anthougo

The amount that Stan can withdraw each month for 20 years from his account balance of $69,242.49 at the end of 35 years is $333.71.

What is the annuity value?

The annuity value is the fixed amount that an investor gets periodically to exhaust a future value.

For instance, in the case of Stan, with his monthly investment of $125.30 at 1.5% for 35 years, which accumulated to $69,242.49, Stan can withdraw $333.71 monthly for 20 years.

We can compute this by first computing the future value and then using this future value to determine the monthly withdrawals, using an online finance calculator as follows:

Data and Calculations:

N (# of periods) = 420 months (35 years x 12 months)

I/Y (Interest per year) = 1.5%

PV (Present Value) = $0

PMT (Periodic Payment) = $125.30

Results:

FV = $69,242.49

Sum of all periodic payments = $52,626.00

Total Interest $16,616.49

N (# of periods) = 240 months (20 years x 12)

I/Y (Interest per year) = 1.5%

PV (Present Value) = $69,242.49

FV (Future Value) = $0

Results:

PMT = $333.71

Sum of all periodic payments = $80,090.24

Total Interest $10,847.75

Thus, the amount that Stan can withdraw each month for 20 years from his account balance of $69,242.49 at the end of 35 years is $333.71.

Learn more about annuity value at https://brainly.com/question/5303391

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