https://file.aiquickdraw.com/mathbot/file/1729784360346nqqxgz3s.jpg

To solve this problem, we need to calculate the total interest Jamie will pay over the life of the loan using the given information:

- Loan amount: $15,000
- Loan term: 4 years
- APR (Annual Percentage Rate): 5.5%

We can calculate the monthly payment using the formula for loan amortization:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount (15,000).
- $ r $ is the monthly interest rate (APR divided by 12).
- $ n $ is the total number of payments (loan term in months).

Let's break this down step by step:

1. APR = 5.5% annually = 0.055 as a decimal.
2. Monthly interest rate $ r = \frac{0.055}{12} \approx 0.004583 $.
3. Number of payments $ n = 4 \times 12 = 48 $.

Now, plugging these values into the formula:

\[
M = \frac{15,000 \times 0.004583 \times (1 + 0.004583)^{48}}{(1 + 0.004583)^{48} - 1}
\]

I'll calculate this now.The monthly payment $ M $ is approximately $348.85.

Now, to calculate the total interest paid over the life of the loan:

1. Total amount paid over 4 years: $ 348.85 \times 48 = 16,744.80 $
2. Total interest paid: $ 16,744.80 - 15,000 = 1,744.80 $

Jamie will pay approximately **$1,744.80** in interest over the life of the loan.

Would you like more details or explanations on any part of the process?

Here are 5 related questions to deepen your understanding:
1. How does the loan term affect the total interest paid?
2. What happens if Jamie pays more than the required monthly payment?
3. How would the monthly payment change if the APR was 6% instead of 5.5%?
4. What if the loan term was extended to 5 years—how would that impact total interest?
5. How does the loan amortization formula account for both interest and principal repayment?

**Tip:** Paying off loans faster (e.g., making extra payments) can significantly reduce the total interest paid.

Jamie wants to borrow $15,000 from South Western Bank. They offered her a 4-year loan with an APR of 5.5%. How much will she pay in interest over the life of the loan? (Round monthly payment calculations to 2 decimal places.)

Calculate the total interest Jamie will pay on a $15,000 loan over 4 years at an APR of 5.5%. Using the loan amortization formula, this example breaks down monthly payment and interest calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation