Consider a student loan of ​$17,500 at a fixed APR of 6​% for 30 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.

To calculate the monthly payment, total amount paid, and the breakdown of principal versus interest for a loan, we will use the **loan amortization formula**. The loan is for **$17,500** at a **fixed APR of 6%** over **30 years**.

### a. Monthly Payment Calculation

The formula for calculating the monthly payment $ M $ is:

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

Where:
- $ P $ is the loan amount ($17,500),
- $ r $ is the monthly interest rate (annual rate divided by 12 months),
- $ n $ is the total number of payments (loan term in months, i.e., 30 years $\times$ 12).

Let's plug in the values:
- $ P = 17,500 $,
- Annual interest rate = 6%, so $ r = \frac{6}{12 \times 100} = 0.005 $ per month,
- $ n = 30 \times 12 = 360 $ months.

Now, I will calculate the monthly payment.The monthly payment for the loan is approximately **$104.92**.

### b. Total Amount Paid Over the Loan Term

To calculate the total amount paid over the term of the loan, we simply multiply the monthly payment by the total number of payments:

\[
\text{Total Paid} = M \times n
\]

Let me calculate that for you.The total amount paid over the term of the loan is approximately **$37,771.68**.

### c. Percentage of Total Paid Toward Principal and Interest

To determine the percentage paid toward the principal and the interest, we can calculate the following:

- **Total interest paid**: $ \text{Total Paid} - P $
- **Percentage toward principal**: $ \frac{P}{\text{Total Paid}} \times 100 $
- **Percentage toward interest**: $ \frac{\text{Total Interest Paid}}{\text{Total Paid}} \times 100 $

Let me compute these percentages for you.Of the total amount paid:
- **46.33%** is paid toward the principal.
- **53.67%** is paid toward interest.

### Summary:
- **Monthly payment**: $104.92
- **Total amount paid**: $37,771.68
- **Percentage toward principal**: 46.33%
- **Percentage toward interest**: 53.67%

Would you like further details or have any questions?

Here are some related questions for further understanding:
1. How would the monthly payment change if the interest rate were reduced to 5%?
2. What if the loan term were shortened to 20 years with the same interest rate?
3. How is interest calculated on an amortizing loan versus a simple interest loan?
4. What is the impact of making an extra monthly payment on reducing total interest?
5. How can refinancing a student loan affect the loan's overall cost?

**Tip**: Making extra payments toward the principal early in the loan term can reduce the total interest paid over time.

Learn how to calculate the monthly payment, total amount paid, and the breakdown between principal and interest for a $17,500 loan at 6% APR over 30 years. This problem involves key finance concepts such as loan amortization and interest calculation. Ideal for Grades 10-12 and college-level students.

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