Consider a student loan of ​$15,000 at a fixed APR of 6​% for 4 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 solve this problem, we’ll use the standard amortization formula for a loan to determine the monthly payment and the total amount paid. Let’s go step by step.

### Given:
- Loan amount ($ P $): $15,000
- Annual Percentage Rate (APR): 6% (or 0.06 as a decimal)
- Loan term: 4 years
- Number of payments per year: 12 (since payments are monthly)
- Total number of payments ($n$): $ 4 \times 12 = 48 $

### a. 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 $ is the loan amount ($15,000),
- $ r $ is the monthly interest rate, which is the annual rate divided by 12, i.e., $ r = \frac{0.06}{12} = 0.005 $,
- $ n $ is the total number of payments (48).

Let me calculate the monthly payment.Let's manually recalculate the monthly payment step-by-step.

1. First, calculate the monthly interest rate $ r $:
\[
r = \frac{0.06}{12} = 0.005
\]

2. Now calculate the total number of payments over 4 years:
\[
n = 4 \times 12 = 48
\]

3. Plugging the values into the monthly payment formula:
\[
M = \frac{15000 \times 0.005 \times (1+0.005)^{48}}{(1+0.005)^{48} - 1}
\]

Now, I'll proceed to simplify and compute this for you.

It seems there’s a delay in calculating directly. I'll guide you through the calculation manually instead.

Let's break it down:

1. First, calculate $ (1 + r)^{n} $:
\[
(1 + 0.005)^{48} = 1.005^{48} \approx 1.270244
\]

2. Now, calculate the numerator of the formula:
\[
15000 \times 0.005 \times 1.270244 = 95.2683
\]

3. Then, calculate the denominator:
\[
1.270244 - 1 = 0.270244
\]

4. Finally, divide the numerator by the denominator:
\[
M = \frac{95.2683}{0.270244} \approx 352.57
\]

So, the monthly payment is approximately **$352.57**.

---

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

To calculate the total amount paid over the term of the loan:
\[
\text{Total Amount Paid} = M \times n
\]
Where $ M = 352.57 $ and $ n = 48 $.

Let me calculate this for you.To manually calculate the total amount paid:

\[
\text{Total Amount Paid} = 352.57 \times 48 = 16923.36
\]

So, the total amount paid over the loan term is approximately **$16,923.36**.

---

### c. Percentage Paid Toward Principal and Interest

- **Amount paid toward principal**: The principal is the original loan amount, which is $15,000.
- **Amount paid toward interest**: The total interest paid is the total amount paid minus the principal:
\[
\text{Interest Paid} = 16,923.36 - 15,000 = 1,923.36
\]

To calculate the percentage of the total amount paid toward the principal and the interest:

- Percentage paid toward the principal:
\[
\frac{15,000}{16,923.36} \times 100 \approx 88.64\%
\]

- Percentage paid toward interest:
\[
\frac{1,923.36}{16,923.36} \times 100 \approx 11.36\%
\]

---

### Summary:
a. Monthly payment: **$352.57**  
b. Total amount paid: **$16,923.36**  
c. Percentage toward principal: **88.64%**, percentage toward interest: **11.36%**

Would you like further details on any part of this calculation?

Here are some related questions:
1. How does the interest rate affect the monthly payment?
2. What would happen if the loan term increased?
3. How is compound interest incorporated in this calculation?
4. What is the difference between simple and compound interest for loans?
5. How can extra payments reduce the total interest paid?

**Tip**: Making additional payments towards the principal early in the loan term can reduce the total interest you pay over time.

Consider a student loan of ​$15,000 at a fixed APR of 6​% for 4 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 for a $15,000 student loan at 6% APR over 4 years. This example explains loan amortization, interest, and principal percentage calculations. Includes step-by-step guide for Grades 10-12.

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