To calculate Laura's monthly payment and total finance charge over the term of her loan, let's follow these steps:
1. Identify Key Figures:
- Loan Amount: \[tex]$25,000
- Interest Rate: 7.5%
- Term: 5 years (60 months)
2. Monthly Payment Calculation:
From the provided amortization table, the monthly payment per \$[/tex]1,000 of loan for a 7.5% interest rate over 5 years is \[tex]$20.04.
To find the total monthly payment, we multiply this rate by the loan amount in increments of \$[/tex]1,000:
[tex]\[
\text{Monthly Payment} = \$20.04 \times \left(\frac{\$25,000}{1000}\right) = \$20.04 \times 25 = \$501.00
\][/tex]
3. Total Finance Charge Calculation:
The total finance charge is the difference between the total amount paid over the term of the loan and the initial loan amount.
First, find the total payment over the entire loan term (5 years):
[tex]\[
\text{Total Payment} = \text{Monthly Payment} \times \text{Number of Months} = \$501.00 \times 60 = \$30,060.00
\][/tex]
Next, calculate the finance charge:
[tex]\[
\text{Finance Charge} = \text{Total Payment} - \text{Loan Amount} = \$30,060.00 - \$25,000.00 = \$5,060.00
\][/tex]
So, Laura's monthly payment will be \[tex]$501.00, and her total finance charge over the course of the loan will be \$[/tex]5,060.00.
