Tomasz purchased a new heating and air-conditioning system for his home and financed $7,100 at an annual interest rate of 2.8% 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, we first need to determine the future value of the loan using the compound interest formula, and then subtract the original loan amount from the future value.

### Compound Interest Formula:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $ A $ is the amount of money accumulated after $ t $ years (future value),
- $ P $ is the principal amount (the initial loan),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the time the money is invested or borrowed for (in years).

### Given Values:
- $ P = 7,100 $
- $ r = 2.8\% = 0.028 $
- $ n = 12 $ (monthly compounding)
- $ t = 3 $ years

### Step 1: Calculate the future value $ A $.
\[
A = 7,100 \left(1 + \frac{0.028}{12}\right)^{12 \times 3}
\]

### Step 2: Calculate the interest paid.
The total interest paid is the difference between the future value $ A $ and the principal $ P $:
\[
\text{Interest} = A - P
\]

Let's compute this.Tomasz will pay approximately **$621.41** in interest over the term of the loan.

Would you like further details on the calculations or any additional clarifications?

Here are five related questions to expand your understanding:
1. How does increasing the interest rate affect the total interest paid?
2. What would happen to the interest if the loan period was extended to 5 years?
3. How does the frequency of compounding (e.g., quarterly instead of monthly) impact the future value?
4. How much would Tomasz save if he made an additional payment toward the principal each month?
5. What would be the difference if Tomasz financed the same amount with a simple interest loan?

**Tip**: Increasing the number of compounding periods (like switching from monthly to daily compounding) generally increases the total interest paid due to more frequent accumulation of interest.

Tomasz purchased a new heating and air-conditioning system for his home and financed $7,100 at an annual interest rate of 2.8% compounded monthly for 3 years. How much interest (in dollars) will Tomasz pay over the term of the loan?

Learn how to calculate the interest on a $7,100 loan with a 2.8% annual rate compounded monthly for 3 years. This problem demonstrates the compound interest formula, key finance concepts, and exponential growth, making it suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation