If Barbara loans $7,500 and makes payments of $100 plus 9% interest, what is her first month's payment?

To determine the first month's payment Barbara must make on the loan, we need to break down the components of her payment.

First, the loan amount is $7,500, and the interest rate is 9% per annum. To calculate the monthly interest charge, we begin by converting the annual interest rate to a monthly rate. This is done by dividing the annual rate by 12 months.

The monthly interest rate is: [ \text{Monthly Interest Rate} = \frac{9%}{12} = 0.75% ]

Next, we calculate the interest for the first month based on this monthly interest rate: [ \text{Monthly Interest} = \text{Loan Amount} \times \text{Monthly Interest Rate} ] [ \text{Monthly Interest} = 7,500 \times 0.0075 = 56.25 ]

Now we add the fixed repayment amount of $100 to this calculated interest to find the total payment for the first month: [ \text{First Month's Payment} = \text{Fixed Payment} + \text{Monthly Interest} ] [ \text{First Month's Payment} = 100 +