To calculate the principal repaid by the 17th monthly payment of $750 on a $22,000 loan at 15% compounded monthly, we need to calculate the monthly interest rate, the remaining balance after 16 payments, and the interest portion of the 17th payment.
The monthly interest rate is calculated by dividing the annual interest rate by the number of compounding periods per year. In this case, it would be 15% / 12 = 1.25%.
The remaining balance after 16 payments can be calculated using the loan balance formula:
![$$B = P(1 + r)^n - (PMT/r)[(1 + r)^n - 1]$$](https://img.qammunity.org/2024/formulas/mathematics/high-school/wyc5etmxmytxmtvy1lp9eof8cdl0phvl77.png)
Where B is the remaining balance, P is the initial principal, r is the monthly interest rate, n is the number of payments made, and PMT is the monthly payment amount.
Substituting the values into the formula, we get:
![$$B = 22000(1 + 0.0125)^(16) - (750/0.0125)[(1 + 0.0125)^(16) - 1]$$](https://img.qammunity.org/2024/formulas/mathematics/high-school/4yvoa2968s9m8o3kdvuxi1ermrp22ar4fq.png)
After calculating this expression, we find that the remaining balance after 16 payments is approximately $17,135.73.
The interest portion of the 17th payment can be calculated by multiplying the remaining balance by the monthly interest rate: $17,135.73 * 0.0125 = $214.20.
Therefore, the principal repaid by the 17th payment is $750 - $214.20 = $535.80.