Answer:
you would be able to withdraw $3859.08 each month for 25 years
Explanation:
Payout annuity are normally used for retirements for example you have $500,000 saved for retirement, your account earns 8% interest and you want to take money out each month for about 27 years. The Payout Annuity Formula is given by:
[tex]P_{o}=\frac{d(1-(1+\frac{r}{k})^{-NK} )}{(\frac{r}{k} )}[/tex]
Where:
P₀ = balance in the account at the beginning (starting amount, or principal).
d = regular withdrawal amount (the amount you take out each year, each month, etc.)
r = annual interest rate
k = number of compounding periods in one year.
N = number of years we plan to take withdrawals.
From the question, it is given that:
P₀ = $500,000
r = 8% = 0.08
k = 12 (for one year)
N = 25
d = ?
[tex]P_{o}=\frac{d(1-(1+\frac{r}{k})^{-NK} )}{(\frac{r}{k} )}[/tex]
substituting values,
[tex]500000=\frac{d(1-(1+\frac{0.08}{12})^{-25*12} )}{(\frac{0.08}{12} )}[/tex]
[tex]500000=\frac{d(1-0.1362 )}{(\frac{0.08}{12} )}[/tex]
[tex]500000=\frac{0.8638d}{0.0067}[/tex]
[tex]500000=129.5645d[/tex]
d = $3859.08
Therefore, you would be able to withdraw $3859.08 each month for 25 years
