Chiara purchased a new natural gas barbecue for $2,750 and made a down payment that was 30% of the purchase price. She financed the remaining balance for 9 months at an annual interest rate of 5.5% compounded monthly. What is Chiara's monthly payment? (Round your answer to the nearest cent.)

We can determine Chiara's monthly payment by breaking the problem into steps and using the formula for the monthly payment of a loan.

### Step 1: Calculate the down payment
Chiara made a down payment that was 30% of the purchase price.

\[
\text{Down Payment} = 30\% \times 2750 = 0.30 \times 2750 = 825
\]

### Step 2: Calculate the loan amount
The loan amount is the remaining balance after the down payment.

\[
\text{Loan Amount} = 2750 - 825 = 1925
\]

### Step 3: Calculate the monthly interest rate
The annual interest rate is 5.5%, but since the interest is compounded monthly, we need to convert this to a monthly interest rate.

\[
\text{Monthly Interest Rate} = \frac{5.5\%}{12} = \frac{0.055}{12} = 0.0045833
\]

### Step 4: Calculate the number of months
The loan is financed for 9 months, so:

\[
n = 9
\]

### Step 5: Use the loan payment formula
We will use the standard formula for the monthly payment of a loan:

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

where:
- $M$ is the monthly payment
- $P$ is the loan amount ($P = 1925$)
- $r$ is the monthly interest rate ($r = 0.0045833$)
- $n$ is the number of months ($n = 9$)

Let’s calculate the monthly payment.Chiara's monthly payment is approximately \$218.82.

Would you like more details or further explanations? Here are 5 related questions you might explore:

1. How is the monthly interest rate derived from the annual rate?
2. What if Chiara made a higher down payment—how would her monthly payment change?
3. How would extending the loan term to 12 months affect the monthly payment?
4. How does compound interest affect the total amount paid over time?
5. What happens if the interest rate changes midway through the loan?

**Tip:** When calculating loan payments, always make sure to use the correct time period for interest rates—monthly, quarterly, etc., depending on how often the interest is compounded.

Learn how to calculate Chiara's monthly loan payment for her $2,750 natural gas barbecue. With a 30% down payment, a 9-month loan period, and an annual interest rate of 5.5% compounded monthly, this step-by-step solution walks through key loan concepts and formulas. Perfect for students in Grades 10-12.

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