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

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

• A. $109
• B. $156.25
• C. $162.50
• D. $167.50

Answer: (B)

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 +

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 +