File Edit Format View Help Jennifer Kaufman bought a used Toyota Prius for \( \$ 18,500 \). She made a \( \$ 3,500 \) down payment and is financing the balance at a particular bank over a 3 year period at \( 12 \% \) interest. As her banker, calculate what equal monthly payments (in \( \$ \) ) will be required by Jennifer to amortize the car loan. (Round your answer to the nearest cent.)

To calculate Jennifer's equal monthly payments, we first need to determine the loan amount. She bought the Prius for \( \$ 18,500 \) and made a down payment of \( \$ 3,500 \), so: \[ \text{Loan Amount} = 18500 - 3500 = 15000 \] Next, we use the loan amortization formula, which is: \[ M = P \frac{r(1 + r)^n}{(1 + r)^n - 1} \] Where: - \( M \) is the monthly payment - \( P \) is the loan amount (\$ 15,000) - \( r \) is the monthly interest rate (annual rate / 12 months) - \( n \) is the total number of payments (loan term in months) The annual interest rate is \( 12\% \), so the monthly rate \( r \) is: \[ r = \frac{12\%}{12} = 0.01 \] Since she is financing the loan for 3 years, the total number of payments \( n \) is: \[ n = 3 \times 12 = 36 \] Now we can plug these numbers into the formula: \[ M = 15000 \frac{0.01(1 + 0.01)^{36}}{(1 + 0.01)^{36} - 1} \] Calculating \( (1 + 0.01)^{36} \): \[ (1.01)^{36} \approx 1.430768 \] Now substitute this value back into the formula: \[ M = 15000 \frac{0.01 \times 1.430768}{1.430768 - 1} \] \[ = 15000 \frac{0.01430768}{0.430768} \] \[ = 15000 \times 0.033227644 \] \[ \approx 498.41466 \] Rounding this to the nearest cent, the monthly payments Jennifer needs to make are approximately: \[ \text{Monthly Payment} \approx \$ 498.41 \]