Tomasz purchased a new heating and air-conditioning system for his home and financed $6,700 at an annual interest rate of 4.4% compounded monthly for 3 years. How much interest (in dollars) will Tomasz pay over the term of the loan?

To calculate the total interest Tomasz will pay on the loan, we can use the **compound interest formula**:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of the loan after interest (future value),
- $ P $ is the principal (the initial loan amount),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years.

### Step 1: Identify the values
- $ P = 6,700 $ dollars (principal),
- $ r = 4.4\% = 0.044 $,
- $ n = 12 $ (since the interest is compounded monthly),
- $ t = 3 $ years.

### Step 2: Plug the values into the formula

\[
A = 6700 \left(1 + \frac{0.044}{12}\right)^{12 \times 3}
\]

### Step 3: Calculate $ A $

Let's first calculate $ A $, then subtract the principal $ P $ from $ A $ to find the total interest Tomasz will pay. I'll do the calculations now.

Tomasz purchased a new heating and air-conditioning system for his home and financed $6,700 at an annual interest rate of 4.4% compounded monthly for 3 years. How much interest (in dollars) will Tomasz pay over the term of the loan?

Find out how to calculate the total interest on a $6,700 loan with an annual interest rate of 4.4% compounded monthly over 3 years. Learn how to apply the compound interest formula to solve this finance math problem, suitable for high school students (Grades 10-12).

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