7. Suppose that you decide to buy a car for $$ \$ 39,635 $$, including faxes and icense 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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Let

$$
P = \$39\,635,\quad D = \$9\,000,\quad \text{Annual interest rate} = 1.99\%.
$$

1. First, compute the amount financed (the principal of the loan):

$$
L = P - D = 39\,635 - 9\,000 = 30\,635.
$$

2. The loan is for 5 years, which is

$$
n = 5 \times 12 = 60 \text{ months}.
$$

3. The monthly interest rate is

$$
r = \frac{0.0199}{12} \approx 0.00165833.
$$

4. The monthly payment for an installment loan is given by

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

5. First, compute the factor $$(1+r)^n$$:

$$
(1+r)^n = \left(1+0.00165833\right)^{60}.
$$

Using a precise calculation (or an approximation via the exponential),

$$
(1+0.00165833)^{60} \approx 1.10452.
$$

6. Now plug the values into the formula:

$$
M = 30\,635 \cdot \frac{0.00165833 \times 1.10452}{1.10452 - 1}.
$$

Calculate the numerator:

$$
0.00165833 \times 1.10452 \approx 0.001831,
$$

and then

$$
30\,635 \times 0.001831 \approx 56.18.
$$

The denominator is

$$
1.10452 - 1 = 0.10452.
$$

Thus, the monthly payment is

$$
M \approx \frac{56.18}{0.10452} \approx 537.38.
$$

So, the monthly payment is approximately

$$
\$537.38.
$$

7. The total amount paid over the life of the loan is

$$
\text{Total paid} = M \times n \approx 537.38 \times 60 \approx 32\,242.80.
$$

8. The total interest paid is the difference between the total paid and the financed amount:

$$
\text{Total interest} \approx 32\,242.80 - 30\,635 \approx 1\,607.80.
$$

Thus, the answers are:

- Monthly payment: approximately $$\$537.38$$.
- Total interest: approximately $$\$1\,607.80$$.
The monthly payment is approximately \$537.38, and the total interest over the loan period is approximately \$1,607.80.

Suppose that you decide to buy a car for , including faxes and
icense 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 faxes and icense 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.