Consider a student loan of ​$5 comma 000 at a fixed APR of 6​% for 2 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. (Do not round until the final answer. Then round to the nearest cent as​ needed.)

We can break the problem into three parts as per the given tasks. Let's go step by step:

**Given:**
- Loan amount (Principal, $ P $): \$5,000
- Annual Percentage Rate (APR): 6% (or 0.06 as a decimal)
- Loan term: 2 years
- Monthly payments (n): 12 payments per year, so $ 2 \times 12 = 24 $ payments in total.

We will use the formula for the monthly payment on an amortized loan:

\[
M = \frac{P \times \frac{r}{12}}{1 - \left(1 + \frac{r}{12}\right)^{-n}}
\]

Where:
- $ M $ is the monthly payment
- $ P $ is the principal
- $ r $ is the annual interest rate
- $ n $ is the total number of payments

Let's solve for $ M $ first:

### a. Monthly Payment Calculation

\[
M = \frac{5000 \times \frac{0.06}{12}}{1 - \left(1 + \frac{0.06}{12}\right)^{-24}}
\]

Let me compute this.The monthly payment ($ M $) is approximately \$221.60.

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

The total amount paid over the term of the loan is the monthly payment multiplied by the total number of payments:

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

Let me compute that.The total amount paid over the term of the loan is approximately \$5,318.47.

### c. Percentage Paid Toward Principal and Interest

1. **Amount Paid Toward Principal**: This is simply the original loan amount, which is \$5,000.
   
2. **Amount Paid Toward Interest**: This is the difference between the total amount paid and the principal.

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

Finally, to find the percentage paid toward the principal and interest:

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

Let's calculate these values.The breakdown of the total amount paid is as follows:

- **Amount paid toward interest**: \$318.47
- **Percentage toward principal**: 94.01%
- **Percentage toward interest**: 5.99%

Would you like further details or have any questions?

Here are some related questions:
1. How does the loan term affect the total interest paid?
2. What happens to the monthly payment if the APR increases to 7%?
3. How would the total interest change if the loan term was 5 years instead of 2 years?
4. How is the monthly payment calculated for a loan with a variable interest rate?
5. What are the differences between simple interest and amortized loan payments?

**Tip**: Extending the loan term reduces monthly payments but increases the total interest paid over time.

Consider a student loan of $5,000 at a fixed APR of 6% for 2 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 interest breakdown for a $5,000 student loan with a 6% APR over 2 years. This problem covers loan amortization, interest rate calculations, and percentage breakdowns, making it suitable for high school students in Grades 10-12.

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