Aidan wants to pay off the loan on his refrigerated trailer on which he has made 15 payments. If Aidan's monthly payment is $297.79 on a 3-year loan at an annual percentage rate of 6.5%, what is the payoff amount (in dollars)?

To calculate Aidan's payoff amount after making 15 payments, we need to calculate the remaining balance of his loan. We'll use the formula for the remaining balance on a loan:

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

Where:
- $ B $ is the remaining balance (payoff amount),
- $ P $ is the monthly payment,
- $ r $ is the monthly interest rate,
- $ n $ is the number of remaining payments.

Let's break it down step by step:

1. **Determine the monthly interest rate $ r $:**
   - Annual percentage rate (APR) is 6.5%, so the monthly interest rate is:
   \[
   r = \frac{6.5\%}{12} = \frac{0.065}{12} = 0.0054167
   \]

2. **Determine the total number of payments:**
   - A 3-year loan means 36 monthly payments in total.

3. **Determine the number of remaining payments:**
   - After making 15 payments, there are $ 36 - 15 = 21 $ payments remaining.

4. **Apply the formula to calculate the remaining balance.**

I will now compute the result.Aidan's payoff amount for the loan, after making 15 payments, is approximately **$5,895.96**.

Would you like any more details or clarifications? 

Here are 5 related questions to explore:
1. How would the payoff amount change if the interest rate were higher or lower?
2. What is the total interest paid over the full term of the loan?
3. How would the monthly payment change if the loan term were 5 years instead of 3 years?
4. Can the loan be paid off earlier by making extra payments, and how does that affect the payoff amount?
5. What if Aidan wants to refinance the loan; how would that affect his payments?

**Tip:** Paying extra toward the loan's principal can reduce the overall interest paid and shorten the loan term.

Learn how to calculate the remaining balance on a loan after 15 payments. This example involves a 3-year loan at 6.5% APR with a monthly payment of $297.79. We explain key concepts like loan amortization, interest rate calculations, and provide a detailed step-by-step solution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation