To determine her maximum possible monthly withdrawal, we need to calculate the balance of her retirement account at the time of retirement and then use that balance to make calculations for her monthly withdrawals.
To calculate the balance of her retirement account at retirement, we can use the formula for future value of an annuity:
FV = PMT x [(1 + (r/n))^(n*t) - 1] / (r/n)
where PMT = $400, r = 9% (interest rate), n = 12 (number of compounding periods per year), and t = 49 (number of years).
FV = $400 x [(1 + (0.09/12))^(12*49) - 1] / (0.09/12)
FV = $2,699,515.33
So her retirement account balance at retirement is estimated to be $2,699,515.33.
Next, we need to calculate the monthly withdrawal amount she can take for 31 years from this retirement account balance. To do this, we can use the formula for fixed periodic payments:
PMT = (r/n) x PV / [1 - (1 + r/n)^(-n*t)]
where PMT = the monthly withdrawal amount, r = 4% (interest rate), n = 12 (number of compounding periods per year), t = 31 (number of years), and PV = $2,699,515.33 (present value or starting balance).
PMT = (0.04/12) x $2,699,515.33 / [1 - (1 + 0.04/12)^(-12*31)]
PMT = $9,606.24
So her maximum possible monthly withdrawal amount, given these assumptions, is approximately $9,606.24.
A woman, with her employer's matching program, contributes $400 at the end of each month to her retirement account, which earns 9% interest, compounded monthly. When she retires after 49 years, she plans to make monthly withdrawals for 31 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)?
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