Consider a student loan of ​$15 comma 000 at a fixed APR of 9​% for 25 years.
a. Calculate the monthly payment. ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
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.

This problem deals with calculating the monthly payment for a loan, the total amount paid over the life of the loan, and the breakdown between principal and interest payments. We can use the **loan amortization formula** for fixed-rate loans to calculate the monthly payment.

The formula for the monthly payment $ M $ is:

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

where:
- $ P $ = loan principal = $15,000
- $ r $ = monthly interest rate = $ \frac{\text{APR}}{12} $
- $ n $ = total number of payments = $ \text{years} \times 12 $

Let's break this into parts:

### Part (a) Calculate the monthly payment:

1. **Loan principal, $ P $**: $15,000
2. **APR**: 9% → Monthly interest rate, $ r = \frac{9\%}{12} = 0.0075 $
3. **Loan term, $ n $**: 25 years → Total number of payments = $ 25 \times 12 = 300 $

We'll substitute these values into the formula to calculate the monthly payment $ M $.

### Part (b) Total amount paid over the term of the loan:

The total amount paid is simply the monthly payment $ M $ multiplied by the number of payments $ n $.

\[
\text{Total amount paid} = M \times n
\]

### Part (c) Breakdown between principal and interest:

1. **Total amount paid**: This is the total of all monthly payments over the loan term (calculated in part (b)).
2. **Amount paid toward interest**: This is the total amount paid minus the original loan principal $ P $.
3. **Percentage of payments toward principal**: 
   \[
   \frac{P}{\text{Total amount paid}} \times 100
   \]
4. **Percentage of payments toward interest**:
   \[
   \frac{\text{Interest paid}}{\text{Total amount paid}} \times 100
   \]

Let me calculate the required values for each part.### Part (a) Monthly Payment:
The monthly payment is approximately **$125.88**.

### Part (b) Total Amount Paid Over the Loan Term:
The total amount paid over the 25-year loan is approximately **$37,763.84**.

### Part (c) Breakdown of Payments:
- **Percentage paid toward the principal**: Approximately **39.72%**.
- **Percentage paid toward interest**: Approximately **60.28%**.

This means that about 60% of the total payments will go towards interest, and about 40% will go towards repaying the loan principal.

Would you like further clarification or details on any part of this solution? Here are 5 related questions for deeper understanding:

1. How would the monthly payment change if the APR were reduced to 7%?
2. What happens to the total interest paid if the loan term is shortened to 20 years?
3. How can early repayments affect the total interest paid over the loan term?
4. What would the monthly payment be for a loan of $20,000 at the same APR and term?
5. How does increasing the loan principal impact the monthly payment and interest?

**Tip**: Always aim to make extra payments towards the principal early in a loan term to reduce the total interest paid.

Consider a student loan of $15,000 at a fixed APR of 9% for 25 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.

Calculate the monthly payment for a $15,000 student loan at 9% APR for 25 years. Learn how to determine the total amount paid, and see the breakdown of payments between principal and interest. This solution includes key concepts like loan amortization and percentage calculations. Suitable for high school students in Grades 11-12.

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