Consider a student loan of ​$12,500 at a fixed APR of 6% for 20 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for interest.
Question content area bottom
Part 1
a. The monthly payment is ​$enter your response here. 
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)
Part 2
b. The total payment over the term of the loan is ​$enter your response here.
​(Round to the nearest cent as​ needed.)
Part 3
c. Of the total payment over the term of the​ loan, enter your response here​% is paid toward the principal and enter your response here​% is paid toward interest.
​(Round to the nearest tenth as​ needed.)

This problem involves calculating the monthly payments, total payment, and interest and principal portions for a loan, using the formula for a fixed-rate loan (such as a student loan). The formula to calculate the monthly payment $ M $ is:

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

Where:
- $ P $ is the loan amount (the principal),
- $ r $ is the monthly interest rate (annual interest rate divided by 12),
- $ n $ is the total number of payments (loan term in years multiplied by 12).

Let's solve this step by step.

### Part 1: Calculate the monthly payment

Given:
- $ P = 12,500 $ (loan amount),
- Annual interest rate $ = 6\% $, so $ r = \frac{6\%}{12} = 0.005 $ (monthly interest rate),
- Loan term $ = 20 $ years, so $ n = 20 \times 12 = 240 $ months.

Substitute these values into the formula and solve for $ M $.

Let me calculate that for you.The monthly payment for the loan is approximately **$89.55**.

### Part 2: 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 number of months:

\[
\text{Total Payment} = M \times n
\]

Let me calculate that for you.The total amount paid over the term of the loan is approximately **$21,492.93**.

### Part 3: Percentage paid toward principal and interest

To find the percentage paid toward the principal and interest:

- The percentage paid toward the principal is:

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

- The percentage paid toward interest is:

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

Let me calculate both percentages for you.- **58.2%** of the total payment is paid toward the principal.
- **41.8%** of the total payment is paid toward interest.

### Summary:
- a. The monthly payment is **$89.55**.
- b. The total payment over the term of the loan is **$21,492.93**.
- c. Of the total payment, **58.2%** is paid toward the principal, and **41.8%** is paid toward interest.

Do you have any questions or would you like further details? 

Here are five related questions:
1. How would the monthly payment change if the loan term was 10 years instead of 20 years?
2. What happens to the monthly payment if the interest rate increases to 8%?
3. How is the interest amount calculated in each payment using amortization?
4. What would be the total interest paid if the loan was paid off in 15 years?
5. How does the principal balance decrease over time with fixed monthly payments?

**Tip**: A shorter loan term typically reduces the total interest paid but increases the monthly payments.

Consider a student loan of $12,500 at a fixed APR of 6% for 20 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 payment, and the breakdown of principal and interest for a $12,500 student loan with a 6% APR over 20 years. Includes step-by-step explanation of formulas and results, suitable for advanced high school or college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation