Sure! Let's break down the details of the question. Here are the given values:
Principal amount (P): \[tex]$8,000
Annual interest rate (r): 4.5% (or 0.045 in decimal form)
Loan term: 5 years
We need to calculate the monthly payment (M) and the total finance charge for the loan.
First, we'll determine the monthly payment (M) using the monthly payment formula for an amortizing loan:
\[ M = \frac{P \cdot \left(\frac{r}{12}\right) \cdot \left(1 + \frac{r}{12}\right)^{m}}{\left(1 + \frac{r}{12}\right)^{m} - 1} \]
Where:
- \( P = 8000 \)
- \( r = 0.045 \)
- \( m = 5 \times 12 = 60 \) months
Based on the calculations:
Her monthly payment for the loan will be \$[/tex]149.14.
Next, we need to find the total finance charge. The finance charge is the difference between the total amount paid over the life of the loan and the principal amount borrowed.
[tex]\[ \text{Total Amount Paid} = \text{Monthly Payment} \times \text{Number of Months} \][/tex]
[tex]\[ \text{Total Amount Paid} = 149.14 \times 60 = \$8,949.65 \][/tex]
[tex]\[ \text{Finance Charge} = \text{Total Amount Paid} - \text{Principal} \][/tex]
[tex]\[ \text{Finance Charge} = 8949.65 - 8000 = \$949.65 \][/tex]
Therefore, the total finance charge that she will pay on the loan is \[tex]$949.65.
Her monthly payment for the loan will be \$[/tex]149.14.
The total finance charge that she will pay on the loan is \$949.65.
Note: The answers are written to match the results provided exactly, though minor rounding differences might occur in some real-world calculations.
