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Jennifer Kaufman bought a used Toyota Prius for . She made a
down payment and is financing the balance at a particular bank
over a 3 year period at 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.)

Ask by Pollard Reeves. in the United States

Mar 21,2025

Question

File Edit Format View Help
Jennifer Kaufman bought a used Toyota Prius for . She made a
down payment and is financing the balance at a particular bank
over a 3 year period at 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.)

Ask by Pollard Reeves. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

We start by noting that Jennifer is financing

$$
P = \$18\,500 - \$3\,500 = \$15\,000.
$$

The annual interest rate is $$ 12\% $$, so the monthly interest rate is

$$
r = \frac{0.12}{12} = 0.01.
$$

The loan term is 3 years, or

$$
n = 3 \times 12 = 36 \text{ months}.
$$

The formula for the monthly payment $$ M $$ to fully amortize a loan is

$$
M = P \times \frac{r(1+r)^n}{(1+r)^n-1}.
$$

Substitute the known values:

$$
M = 15000 \times \frac{0.01(1.01)^{36}}{(1.01)^{36}-1}.
$$

First, we calculate $$(1.01)^{36}$$. Using a calculator, we find

$$
(1.01)^{36} \approx 1.430768.
$$

Now compute the numerator:

$$
0.01 \times (1.01)^{36} \approx 0.01 \times 1.430768 = 0.01430768,
$$
$$
\text{Numerator} = 15000 \times 0.01430768 \approx 214.6152.
$$

Next, calculate the denominator:

$$
(1.01)^{36} - 1 \approx 1.430768 - 1 = 0.430768.
$$

Thus, the monthly payment is

$$
M \approx \frac{214.6152}{0.430768} \approx 498.50.
$$

Jennifer's equal monthly payment is approximately $$\$498.50$$.
Jennifer's monthly payment is approximately \$498.50.