For a fully amortized fixed-rate mortgage of $50,000 at 12% over 30 years with monthly payments of $514.31, what is the principal portion of the first payment?

To determine the principal portion of the first mortgage payment, it's important first to understand how mortgage payments are structured. Each monthly payment consists of two components: interest and principal.

In this case, the mortgage amount is $50,000 with an annual interest rate of 12%. When calculating the interest for the first payment, you use the outstanding loan balance at that time, which is the full $50,000 because it is the first payment.

The monthly interest rate is calculated by dividing the annual rate by 12, which gives us 1% (12% ÷ 12 months). To find the interest portion of the first payment, multiply the outstanding balance ($50,000) by the monthly interest rate (0.01):

Interest for the first month = $50,000 × 0.01 = $500.

Since the total monthly payment is $514.31, the principal portion of the first payment is calculated by taking the total payment and subtracting the interest portion:

Principal portion = Total payment - Interest portion

Principal portion = $514.31 - $500 = $14.31.

Thus, the principal portion of the first payment is $14.31, which is why this choice is correct. Understanding