Question 1190444: A. For all parts of this problem, money is invested in a retirement account with an APR of 8.04%. (This is close to the average annual return rate for a traditional individual retirement account over the last decade.) You want to be able to withdraw $24,000 per year for 20 years after retirement. Round up to the cent for each answer.
How much must you have in the account to start with if compounding and withdrawals are both annual?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Present value of annuity
PV = C*(1 - (1+i)^(-n))/i
C = amount of cash needed per period = $24,000
i = interest rate per period = 0.0804
n = number of periods = 20
Each period is one year.
PV = C*(1 - (1+i)^(-n))/i
PV = 24000*(1 - (1+0.0804)^(-20))/0.0804
PV = 234,935.78356008
PV = 234,935.78
Interpretation:
If you want 20 annual withdrawals of $24,000 spaced into the future, then you must have $234,935.78 currently today (aka present value). Those 20 future payments are equivalent this current present value payment. This is when we take into account the 8.04% interest rate, compounded annually.
Answer: $234,935.78
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