Question

A​ woman, with her​ employer's matching​ program, contributes ​$600 at the end of each month to her retirement​ account, which earns ​5% ​interest, compounded monthly. When she retires after 40 ​years, she plans to make monthly withdrawals for 25 years. If her account earns 4​% ​interest, compounded​ monthly, then when she​ retires, what is her maximum possible monthly withdrawal​ (without running out of​ money)?

Answer 1

We can start by using the future value formula to find the balance in the retirement account after 40 years:

PV = 0 (since she is starting with no money in the account)
PMT = 600 (her monthly contributions)
i = 0.05/12 (monthly interest rate)
n = 40*12 (number of months in 40 years)

FV = PMT * ((1 + i)^n - 1) / i
FV = 600 * ((1 + 0.05/12)^(40*12) - 1) / (0.05/12)
FV = $1,059,695.32

So after 40 years of contributing $600 per month, with 5% monthly compounded interest, her retirement account will have a balance of $1,059,695.32.

Now we need to find the maximum monthly withdrawal she can make for 25 years without running out of money. We can use the present value of an annuity formula to do this:

PV = FV * i / ((1 + i)^n - 1)
PV = 1,059,695.32 * 0.04/12 / ((1 + 0.04/12)^(25*12) - 1)
PV = $4355.87

So the maximum monthly withdrawal she can make for 25 years, with 4% monthly compounded interest, is $4355.87.

Answer 2

amount after 40 years
= 600(1.0041666..^240 - 1)/.0041666.. = 915,612.09
not the answer the bot got

This becomes the PV of an annuity with
i = .04/12 or .00333...
n = 300
Paym = ?

paym(1 - 1.003333..^-300 )/.00333... = 915.612.09
I get payment = $4,832.944

Answer 3

I apologize for the mistake in my initial response. Thank you for correcting me.

I agree with your calculations, and the correct maximum monthly withdrawal she can make for 25 years, with 4% monthly compounded interest, is $4,832.94.