The monthly payments on a 15-year loan of $25,000 at 5.8% interest are $208.27.
(a) What is the total amount paid over the 15 years?
$ 


(b) What is the total amount of interest paid?

To solve this, let’s break down each part of the problem:

### Given Information:
- Loan amount (principal), $ P = 25,000 $
- Loan term = 15 years
- Interest rate = 5.8%
- Monthly payment = $208.27

### Part (a): Total Amount Paid Over 15 Years

The total amount paid over the loan term is the monthly payment multiplied by the number of months in 15 years:

\[
\text{Total Amount Paid} = \text{Monthly Payment} \times \text{Total Number of Months}
\]

Since 15 years = 180 months:

\[
\text{Total Amount Paid} = 208.27 \times 180 = 37,488.60
\]

So, the total amount paid over 15 years is **$37,488.60**.

### Part (b): Total Amount of Interest Paid

To find the total interest paid, we subtract the original loan amount from the total amount paid:

\[
\text{Total Interest Paid} = \text{Total Amount Paid} - \text{Principal}
\]

\[
\text{Total Interest Paid} = 37,488.60 - 25,000 = 12,488.60
\]

So, the total interest paid over the life of the loan is **$12,488.60**.

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Let me know if you need further clarification on any part. Here are some related questions to extend this topic:

1. What would the monthly payment be if the loan term were extended to 20 years?
2. How does the total interest paid change with a different interest rate?
3. What would happen to monthly payments if the loan amount increased to $50,000?
4. How would you calculate the monthly payment using an amortization formula?
5. What is the impact of making additional principal payments each month on total interest paid?

**Tip:** Always remember, reducing the loan term can significantly lower the total interest paid, even if it increases monthly payments.

The monthly payments on a 15-year loan of $25,000 at 5.8% interest are $208.27.
(a) What is the total amount paid over the 15 years?
(b) What is the total amount of interest paid?

Find the total amount paid and total interest for a 15-year loan of $25,000 at 5.8% interest. Monthly payments are $208.27, and this solution covers formulas for calculating both total and interest payments over time. Ideal for Grades 9-12 math students.

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