Consider a student loan of ​$15 comma 00015,000 at a fixed APR of 66​% for 1515 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.

Let's go through the steps to solve each part of this problem:

We are given:

- **Loan Amount** ($ P $) = $15,000
- **Annual Percentage Rate (APR)** = 6%
- **Loan Term** = 15 years

### a. Calculate the monthly payment:

To calculate the monthly payment, we can use the formula for a fixed-rate loan:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount.
- $ r $ is the monthly interest rate (APR divided by 12).
- $ n $ is the total number of payments (loan term in years times 12 months/year).

Given:
- Monthly interest rate $ r = \frac{6\%}{12} = 0.005 $
- Total number of payments $ n = 15 \times 12 = 180 $

We can now calculate the monthly payment.

### b. Determine the total amount paid over the term of the loan:

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

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

### c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest:

The total amount paid toward the principal is the original loan amount, $ P $. The total interest paid is the difference between the total amount paid and the principal.

The percentage paid toward the principal is:

\[
\text{Percentage toward Principal} = \left( \frac{P}{\text{Total Amount Paid}} \right) \times 100
\]

The percentage paid toward interest is:

\[
\text{Percentage toward Interest} = 100\% - \text{Percentage toward Principal}
\]

Let's calculate each part.### Results:

a. The **monthly payment** is approximately \$126.58.

b. The **total amount paid** over the term of the loan is approximately \$22,784.13.

c. Of the total amount paid:
   - **65.84%** is paid toward the principal.
   - **34.16%** is paid toward interest.

Would you like more details or further clarification?

Here are 5 related questions:
1. How does the term length affect the total amount of interest paid?
2. How does a lower interest rate impact the monthly payment?
3. What happens to the monthly payment if the loan term is shortened to 10 years?
4. How does the loan amount affect the percentage of payments toward interest?
5. Can extra monthly payments reduce the total interest paid on a loan?

**Tip**: Making additional payments on a loan can significantly reduce the total interest paid over time!

Consider a student loan of $15,000 at a fixed APR of 6% for 15 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 a 6% APR over 15 years. Learn the total amount paid, and determine the percentage paid toward the principal and interest using loan amortization formulas. Suitable for students in Grades 10-12.

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