7. Suppose that you decide to buy a car for $$ \$ 39,635 $$, including taxes and license fees. You saved $$ \$ 9000 $$ for a down payment and can get a five-year car loan at $$ 1.99 \% $$. Find the monthly payment and the total interest for the loan.

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We start by determining the amount you need to finance. The car’s price is  
$$
\$39,\!635,
$$  
and you made a down payment of  
$$
\$9,\!000.
$$  
Thus, the loan principal $$ P $$ is  
$$
P = 39,\!635 - 9,\!000 = 30,\!635.
$$

The loan is for 5 years, which is  
$$
n = 5 \times 12 = 60 \text{ months}.
$$

The annual interest rate is  
$$
1.99\%,
$$  
so the monthly interest rate $$ r $$ is  
$$
r = \frac{1.99\%}{12} = \frac{0.0199}{12} \approx 0.00165833.
$$

The formula for the monthly payment $$ M $$ is  
$$
M = \frac{P\,r\,(1+r)^n}{(1+r)^n-1}.
$$

First, compute the factor $$(1+r)^n$$:
$$
(1+r)^n = \left(1+0.00165833\right)^{60}.
$$
Using a calculator or approximation,
$$
(1+r)^{60} \approx 1.10448.
$$

Now plug the values into the formula:
$$
M = \frac{30,\!635 \times 0.00165833 \times 1.10448}{1.10448 - 1}.
$$

Calculate the numerator:
$$
30,\!635 \times 0.00165833 \approx 50.792,
$$
$$
50.792 \times 1.10448 \approx 56.101.
$$

The denominator is:
$$
1.10448 - 1 = 0.10448.
$$

Thus, the monthly payment is:
$$
M \approx \frac{56.101}{0.10448} \approx 536.83.
$$

So, the monthly payment is approximately  
$$
\$536.83.
$$

To find the total interest paid over the life of the loan, first compute the total amount paid:
$$
\text{Total Payment} = M \times n = 536.83 \times 60 \approx 32,\!209.80.
$$

Subtract the principal to obtain the total interest:
$$
\text{Total Interest} = 32,\!209.80 - 30,\!635 \approx 1,\!574.80.
$$

Thus, the total interest paid on the loan is approximately  
$$
\$1,\!574.80.
$$
The monthly payment is approximately \$536.83, and the total interest paid over the five-year loan is approximately \$1,574.80.

Suppose that you decide to buy a car for , including taxes and
license fees. You saved for a down payment and can get a five-year car
loan at . Find the monthly payment and the total interest for the loan.

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Suppose that you decide to buy a car for , including taxes and license fees. You saved for a down payment and can get a five-year car loan at . Find the monthly payment and the total interest for the loan.