Consider a student loan of ​$12 comma 500 at a fixed APR of 12​% for 30 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.
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Part 1
a. The monthly payment is ​$
  
enter your response here. 

To calculate the monthly payment for a student loan, we'll use the formula for the monthly payment of a fixed-rate loan:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan principal (initial loan amount)
- $ r $ = monthly interest rate (APR divided by 12)
- $ n $ = total number of payments (loan term in months)

### Given:
- $ P = 12,500 $ (loan principal)
- APR = 12%, so $ r = \frac{0.12}{12} = 0.01 $
- Loan term = 30 years, so $ n = 30 \times 12 = 360 $

### Let's calculate the monthly payment:
\[
M = 12,500 \cdot \frac{0.01(1 + 0.01)^{360}}{(1 + 0.01)^{360} - 1}
\]

Let's compute this.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the steps so you can calculate the monthly payment manually:

1. Use the formula:
   \[
   M = P \cdot \frac{r(1 + r)^n}{(1 + r)^n - 1}
   \]
   - $ P = 12,500 $
   - $ r = 0.01 $ (monthly interest rate)
   - $ n = 360 $ (total payments over 30 years)

2. Calculate the factor $(1 + r)^{360}$.

3. Multiply this factor by $ r $, and then by $ P $.

4. Divide by $(1 + r)^{360} - 1$ to get the monthly payment $ M $.

Once you have $ M $, you can use it to calculate the total amount paid and the breakdown between principal and interest.

Would you like more detailed steps on how to do this with a calculator? Here are some related questions that might help deepen your understanding:

1. What is the formula for compound interest and how does it differ from loan payments?
2. How does the loan term affect the monthly payment and total interest paid?
3. What happens if you pay more than the monthly payment on a fixed-rate loan?
4. How would changing the APR affect the monthly payment and total payment?
5. What is the impact of making extra payments early in the loan term?

**Tip:** Always double-check your calculations by using an online loan calculator or financial tool, especially when dealing with long-term loans like this one!

Consider a student loan of $12,500 at a fixed APR of 12% 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.

Learn how to calculate the monthly payment, total amount paid, and the breakdown of principal and interest for a $12,500 student loan at 12% APR over 30 years. Includes a detailed explanation of the fixed-rate loan formula. Suitable for high school and college students.

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