Question 1190446: 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.
4. How much must you have in the account to start with if compounding and withdrawals are both monthly?
Answer by math_tutor2020(3817)   (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 = $24,000/12 = $2,000
i = interest rate per period = 0.0804/12 = 0.0067 exactly
n = number of periods = 20*12 = 240 months
Each period is one month.
PV = C*(1 - (1+i)^(-n))/i
PV = 2000*(1 - (1+0.0067)^(-240))/0.0067
PV = 238,398.570184098
PV = 238,398.57
Interpretation:
If you want 240 monthly withdrawals of $2,000 spaced into the future (aka $24,000 per year for 20 years), then you must have $238,398.57 currently today. Those 240 future payments are equivalent this current present value payment. This is when we take into account the 8.04% interest rate, compounded monthly.
Answer: $238,398.57
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