7. Suppose that you decide to buy a car for $$ \$ 39,635 $$, induding laxes and license fecs, You saved $$ \$ 0000 $$ for a down payment and can get a five-year car loan at $$ 159 \% $$. Find the monthly payment and the total interest for the laan.

Question

UpStudy AI · Accepted Answer

We first note that since the down payment is $$\$0$$, the entire purchase amount is financed. The loan details are:

- Purchase price (principal): $$P = \$39,\!635$$
- Annual interest rate: $$15.9\%$$ (written as $$0.159$$ in decimal)
- Loan term: 5 years, which is $$n = 5 \times 12 = 60$$ monthly payments

The monthly interest rate is
$$
r = \frac{0.159}{12} \approx 0.01325.
$$

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

Substituting the values we have:
$$
M = 39635 \cdot \frac{0.01325\,(1.01325)^{60}}{(1.01325)^{60}-1}.
$$

### Step 1. Calculate $$(1+r)^n$$
$$
(1.01325)^{60} \approx 2.203.
$$

### Step 2. Compute the numerator and denominator
- Numerator:
  $$
  0.01325 \times 2.203 \approx 0.029191.
  $$
- Denominator:
  $$
  2.203 - 1 = 1.203.
  $$

### Step 3. Calculate the fraction
$$
\frac{0.029191}{1.203} \approx 0.02425.
$$

### Step 4. Compute the monthly payment $$M$$
$$
M = 39635 \cdot 0.02425 \approx 961.15.
$$

Thus, the monthly payment is approximately $$\$961.15$$.

### Step 5. Compute the total payment and total interest
- Total amount paid over the life of the loan:
  $$
  \text{Total Payment} = 60 \times 961.15 \approx 57669.
  $$
- Total interest paid is the total payment minus the principal:
  $$
  \text{Total Interest} \approx 57669 - 39635 = 18034.
  $$

### Final Answers

- Monthly payment: $$\$961.15$$ (approximately)
- Total interest: $$\$18,\!034$$ (approximately)
The monthly payment is approximately \$961.15, and the total interest paid over the five-year loan is approximately \$18,034.

Suppose that you decide to buy a car for , induding laxes and
license fecs, 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 laan.

Upstudy AI Solution

Answer

Solution

Step 1. Calculate

Step 2. Compute the numerator and denominator

Step 3. Calculate the fraction

Step 4. Compute the monthly payment

Step 5. Compute the total payment and total interest

Final Answers

Beyond the Answer

Related Questions

Latest Arithmetic Questions

Suppose that you decide to buy a car for , induding laxes and license fecs, 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 laan.