If John lends Barbara $7500 with a payment plan of $100 plus interest at 9%, which payment includes the lowest principal payment?

To determine which payment includes the lowest principal payment, it is essential to understand how amortization works in a loan with fixed payments. When John lends $7500 to Barbara, she will be making payments that cover both the interest on the loan and a portion of the principal amount.

In the early stages of a loan, the interest component of each payment is generally the highest because it is calculated on the original loan amount. In this case, at 9% interest, the first payment will have a significant portion allocated to interest since it is based on the entire loan amount of $7500. The formula for calculating the interest for the first payment would show that it's substantial, leaving relatively less of the $100 payment to go toward repaying the principal.

As payments progress, the outstanding principal balance decreases, which in turn reduces the interest charge for subsequent payments. This increase in principal repayment will result in more of each subsequent payment being allocated to reducing the principal amount, rather than just covering the interest.

Therefore, the first payment includes the lowest principal payment because, at that point in the loan's life, a larger percentage of the payment goes toward interest rather than reducing the loan balance.