Tomasz purchased a new heating and air-conditioning system for a home and financed $8,800 at an annual interest rate of 2.6% compounded monthly for 3 years. What are Tomasz's monthly payments (in dollars)? (Round your answer to the nearest cent.

To calculate Tomasz's monthly payments for the loan, we use the formula for the monthly payment of a loan with compound interest:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount (principal) = 8800.
- $ r $ is the monthly interest rate (annual rate divided by 12 months).
- $ n $ is the total number of payments (loan term in months).

### Step 1: Convert the annual interest rate to a monthly interest rate.
The annual interest rate is 2.6%, so the monthly interest rate $ r $ is:

\[
r = \frac{2.6\%}{12} = \frac{0.026}{12} = 0.0021667
\]

### Step 2: Calculate the total number of payments.
Since the loan term is 3 years, the total number of payments $ n $ is:

\[
n = 3 \times 12 = 36 \text{ months}
\]

### Step 3: Plug the values into the formula.

\[
M = \frac{8800 \cdot 0.0021667 \cdot (1 + 0.0021667)^{36}}{(1 + 0.0021667)^{36} - 1}
\]

Now, I'll calculate the monthly payment.

Tomasz's monthly payment is approximately **$254.37**.

Would you like further details on how the calculations work or have any other questions?

Here are 5 related questions to explore:
1. How does changing the interest rate affect the monthly payment?
2. What would be the total amount paid after 3 years?
3. How much interest will Tomasz pay over the life of the loan?
4. How would a shorter loan term affect the monthly payment?
5. What if Tomasz makes an extra payment every year—how would that impact the loan?

**Tip**: Making additional payments toward the principal can reduce the total interest paid over the life of the loan.

Tomasz purchased a new heating and air-conditioning system for a home and financed $8,800 at an annual interest rate of 2.6% compounded monthly for 3 years. What are Tomasz's monthly payments (in dollars)? (Round your answer to the nearest cent.)

Find out how to calculate the monthly payments for a $8,800 loan with 2.6% annual interest compounded monthly over 3 years. Using the loan amortization formula, this step-by-step guide covers essential concepts of compound interest and monthly payment calculations, perfect for Grades 10-12 math students.

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