Question 10 You want to buy a $$ \$ 20,000 $$ car. You can make a $$ 10 \% $$ down payment, and will finance the balance with a $$ 3 \% $$ interest rate for 48 months ( 4 years). What will your monthly payments be? $$ \$ $$ Question Help: Video Message instructor Submit Question

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Let the total cost of the car be $$ \$20,\!000 $$.

1. The down payment is $$10\%$$ of $$ \$20,\!000 $$:
   $$
   \$20,\!000 \times 0.10 = \$2,\!000.
   $$

2. The amount to be financed (the balance) is:
   $$
   \$20,\!000 - \$2,\!000 = \$18,\!000.
   $$

3. The annual interest rate is $$3\%$$, so the monthly interest rate is:
   $$
   \frac{3\%}{12} = \frac{0.03}{12} = 0.0025.
   $$

4. The number of monthly payments for 48 months is:
   $$
   n=48.
   $$

5. The formula for the monthly payment for an installment loan is:
   $$
   \text{Payment} = P \cdot \frac{r(1+r)^n}{(1+r)^n-1},
   $$
   where:
   - $$P$$ is the principal financed (here, $$ \$18,\!000 $$),
   - $$r$$ is the monthly interest rate (here, $$0.0025$$),
   - and $$n$$ is the total number of payments (here, $$48$$).

6. Plugging in the values:
   $$
   \text{Payment} = 18000 \cdot \frac{0.0025\,(1+0.0025)^{48}}{(1+0.0025)^{48}-1}.
   $$

7. First, calculate $$(1+0.0025)^{48}$$:
   $$
   (1.0025)^{48} \approx 1.12755.
   $$

8. Substitute back into the formula:
   $$
   \text{Payment} \approx 18000 \cdot \frac{0.0025 \cdot 1.12755}{1.12755 - 1}.
   $$
   Simplify the numerator:
   $$
   18000 \times 0.0025 = 45 \quad \Longrightarrow \quad 45 \times 1.12755 \approx 50.74.
   $$
   Compute the denominator:
   $$
   1.12755 - 1 = 0.12755.
   $$
   Thus:
   $$
   \text{Payment} \approx \frac{50.74}{0.12755} \approx 397.45.
   $$

The monthly payment is approximately $$ \$397.45 $$.
The monthly payment is approximately \$397.45.

Question 10
You want to buy a car. You can make a down payment, and will finance the
balance with a interest rate for 48 months ( 4 years). What will your monthly payments be?

Question Help: Video Message instructor
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Question 10 You want to buy a car. You can make a down payment, and will finance the balance with a interest rate for 48 months ( 4 years). What will your monthly payments be? Question Help: Video Message instructor Submit Question