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Let's work through this problem step by step. We are given the following information:

- The total cost of the car: \$29,000
- The down payment required: 10%
- The loan has a fixed annual interest rate of 8% with monthly payments, over a 2-year (24-month) period.

### (a) Find the required down payment:
To find the down payment, we calculate 10% of the total cost of the car.

\[
\text{Down Payment} = 10\% \times 29,000 = 0.10 \times 29,000 = 2,900
\]

So, the down payment is **\$2,900**.

---

### (b) Find the amount of the auto loan:
The loan amount will be the total cost of the car minus the down payment:

\[
\text{Loan Amount} = 29,000 - 2,900 = 26,100
\]

So, the loan amount is **\$26,100**.

---

### (c) Find the monthly payment:
To find the monthly payment for the loan, we can use the amortization formula:

\[
M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount (\$26,100),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of payments (24 months for a 2-year loan).

First, calculate the monthly interest rate:
\[
r = \frac{8\%}{12} = \frac{0.08}{12} = 0.00667
\]

Now, plug in the values into the formula:
\[
M = \frac{26,100 \cdot 0.00667 \cdot (1 + 0.00667)^{24}}{(1 + 0.00667)^{24} - 1}
\]

Let's calculate the value step by step:
1. $1 + 0.00667 = 1.00667$
2. $1.00667^{24} \approx 1.16988$
3. $(1.00667^{24}) - 1 = 1.16988 - 1 = 0.16988$

Now calculate the numerator:
\[
26,100 \cdot 0.00667 \cdot 1.16988 \approx 203.66
\]

Finally, calculate the monthly payment:
\[
M = \frac{203.66}{0.16988} \approx 1,198.66
\]

So, the monthly payment is approximately **\$1,198.66**.

---

Would you like more details or have any questions? Here are 5 related questions to further explore:

1. What would the monthly payment be if the interest rate were 6% instead of 8%?
2. How much total interest will Mai pay over the course of the loan?
3. What would happen to the monthly payment if the loan term was 3 years instead of 2?
4. How much of the first month's payment goes toward interest, and how much toward the principal?
5. What is the remaining loan balance after 1 year of payments?

### Tip:
When dealing with loans, always break down the terms (interest rate, time period, loan amount) carefully to avoid confusion, especially when switching between annual and monthly rates.

Mai plans to buy a used car that costs $29,000. The dealer requires a 10% down payment. The rest of the cost is financed with a 2-year, fixed-rate amortized auto loan at 8% annual interest with monthly payments. Find the down payment, loan amount, and monthly payment.

Learn how to calculate the down payment, loan amount, and monthly payment for a $29,000 car purchase, with a 10% down payment and 2-year amortized loan at 8% interest. This problem covers key financial formulas, suitable for students in Grades 9-12.

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