You deposit $5,000 per year at the end of each of the next 25 years into an account that pays 8% compounded annually.How much could you withdraw at the end of each of the 20 years following your last deposit if all withdrawals are the same dollar amount? (The twenty-fifth and last deposit is made at the beginning of the 20-year period.The first withdrawal is made at the end of the first year in the 20-year period.)
A) $18,276
B) $27,832
C) $37,230
D) $43,289

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for the future value of an annuity due:

FV = PMT * (((1 + r)^n - 1) / r) * (1 + r)

where PMT is the annual deposit, r is the annual interest rate, and n is the number of years.

First, we need to find the future value of the 25 deposits we will make. We can use the formula:

FV = PMT * (((1 + r)^n - 1) / r)

FV = 5000 * (((1 + 0.08)^25 - 1) / 0.08)
FV = $344,514.62

This means that after 25 years, we will have $344,514.62 in the account.

Next, we need to find the amount that we can withdraw each year for the next 20 years. We can use the formula:

PMT = FV / (((1 + r)^n - 1) / r) * (1 + r)

where FV is the future value we calculated above, n is the number of years we want to withdraw the same amount, and r is the annual interest rate.

We want to withdraw the same amount each year for 20 years, so we set n = 20. The last deposit is made at the beginning of this 20-year period, so we need to add one year to n.

PMT = 344514.62 / (((1 + 0.08)^21 - 1) / 0.08) * (1 + 0.08)
PMT = $37,230.30

This means that we can withdraw $37,230.30 each year for the next 20 years.

Therefore, the best choice is C.

You Deposit $5,000 Per Year at the End of Each