Question

A debt of $6040.66 is repaid by payments of $1066.83 in 8 months, $1107.26 in 13 months, and a final payment in 25 months. If interest was 3% compounded annually, what was the amount of the final payment?

Answer 1

The total amount of the final payment due in 25 months on a debt of $6040.66 with a 3% compound annual interest rate, after accounting for two prior payments, is based on the future value of the remaining debt, illustrating the impact of compound interest over time.

Step-by-step explanation:

To calculate the amount of the final payment on a debt of $6040.66 with a 3% compounded annually interest rate, considering payments of $1066.83 in 8 months, $1107.26 in 13 months, and a final payment in 25 months, we need to find the present value of each payment and the debt to determine what the final payment must be to settle the debt fully.

1. First, we calculate the present value of the first payment of $1066.83, which is due in 8 months.
2. Next, we calculate the present value of the second payment of $1107.26, which is due in 13 months.
3. After accounting for these two payments, we update the total debt to reflect these payments.
4. Finally, we find the future value of the remaining debt after 25 months, which is when the final payment is made, at the 3% annual compound interest rate. This will give us the amount of the final payment required to settle the debt.

It's important to remember that compound interest makes a significant difference over time, as it gains interest on the interest previously earned, as opposed to simple interest which is only on the original principal.