Question

Adam Fowler borrowed $93,860 on March 1, 2018. This amount plus accrued interest at 8% compounded semiannually is to be repaid March 1, 2028. To retire this debt, Adam plans to contribute to a debt retirement fund five equal amounts starting on March 1,2023, and for the next 4 years. The fund is expected to earn 6% per annum. How much must be contributed each year by Adam Fowler to provide a fund sufficient to retire the debt on March 1, 2028? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,583.) Annual contribution to debt retirement fund \$

Answer 1

To retire the debt on March 1, 2028, Adam Fowler must contribute approximately $12,057.91 each year to a debt retirement fund.

Step-by-step explanation:

To determine the amount that Adam Fowler must contribute each year to provide a fund sufficient to retire the debt on March 1, 2028, we can use the formula for the future value of an ordinary annuity:

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

Where:

• FV = Future value of the annuity
• P = Annual contribution
• r = Interest rate per compounding period
• n = Number of compounding periods

In this case, the future value of the annuity needs to be equal to the amount to be repaid, which is $93,860 * (1 + 0.04)^10 = $163,636.81. We also know that the annuity will be contributed for 5 years, and the interest rate per compounding period is 6% divided by 2 since it is compounded semiannually.

Plugging in the values into the formula, we get:

$163,636.81 = P * ((1 + 0.03)^10 - 1) / 0.03

Simplifying the equation, we find that P = $163,636.81 * (0.03 / ((1 + 0.03)^10 - 1)) = $12,057.91

Therefore, Adam Fowler must contribute approximately $12,057.91 each year to provide a fund sufficient to retire the debt on March 1, 2028.