The solution involves calculating the initial amount needed, total money withdrawn, and the interest portion based on annual withdrawals and interest rate.
a) How much do you need in your account at the beginning?
To calculate how much you need at the beginning, you can use the formula for the present value of an ordinary annuity:
PV = PMT [(1 - (1 + r)^-n) / r]
Where PV is the present value, PMT is the annual withdrawal amount, r is the interest rate per period, and n is the number of periods. Plugging in the values: PV = [tex]$30,000 [(1 - (1 + 0.08)^-15) / 0.08]
b) How much total money will you pull out of the account?
To find the total money pulled out, you can simply multiply the annual withdrawal amount by the number of years: $[/tex]30,000 * 15.
c) How much of that money is interest?
The amount of money that is interest can be calculated by subtracting the total amount withdrawn from the initial amount needed in the account.
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