Consider the following loan. Complete parts​ (a)-(c) below.
An individual borrowed ​$84, 000 at an APR of 6​%, which will be paid off with monthly payments of ​$541 for 25 years.
a. Identify the amount​ borrowed, the annual interest​ rate, the number of payments per​ year, the loan​ term, and the payment amount.
The amount borrowed is ​$___, the annual interest rate is ___%, the number of payments per year is ___​, the loan term is ___ ​years, and the payment amount is ​$___.
b. How many total payments does the loan​ require? What is the total amount paid over the full term of the​ loan?
There are ___ payments toward the loan and the total amount paid is ​$___.
c. Of the total amount​ paid, what percentage is paid toward the principal and what percentage is paid for​ interest?
The percentage paid toward the principal is ___% and the percentage paid for interest is ___​%.
​(Round to the nearest tenth as​ needed.)

Let's break down the problem step by step.

### Part (a)
We need to identify the following:

1. **Amount borrowed**: The loan principal is $84,000.
2. **Annual interest rate**: The APR (annual percentage rate) is 6%.
3. **Number of payments per year**: Since the payments are monthly, the number of payments per year is 12.
4. **Loan term**: The loan term is given as 25 years.
5. **Payment amount**: The monthly payment is $541.

So, the answers are:
- The amount borrowed is **$84,000**.
- The annual interest rate is **6%**.
- The number of payments per year is **12**.
- The loan term is **25 years**.
- The payment amount is **$541**.

### Part (b)
Now let's calculate the **total number of payments** and the **total amount paid over the full term** of the loan.

1. **Total number of payments** = $ 12 \times 25 = 300 $ payments.
2. **Total amount paid** = $ 541 \times 300 = 162,300 $ dollars.

Thus:
- There are **300 payments** toward the loan.
- The total amount paid is **$162,300**.

### Part (c)
To find the **percentage paid toward the principal** and **percentage paid for interest**, we use the following:

- The total amount paid is **$162,300**.
- The amount borrowed (principal) is **$84,000**.
- The amount paid toward interest is the total amount paid minus the principal:  
  $ 162,300 - 84,000 = 78,300 $ dollars.

Now, calculate the percentages:
- **Percentage paid toward principal** =  
  $ \left( \frac{84,000}{162,300} \right) \times 100 \approx 51.8\% $.
  
- **Percentage paid toward interest** =  
  $ \left( \frac{78,300}{162,300} \right) \times 100 \approx 48.2\% $.

Thus:
- The percentage paid toward the principal is **51.8%**.
- The percentage paid for interest is **48.2%**.

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Let me know if you'd like more details or have any questions.

Here are some related questions:
1. How does an APR affect the total interest paid on a loan?
2. How would a higher monthly payment affect the loan term and total interest?
3. What is the effect of compounding interest on long-term loans?
4. How does paying extra toward principal impact the loan amortization?
5. What is the formula for calculating monthly payments on a loan?

**Tip**: Always compare the total interest paid over the life of a loan with different APRs to understand the impact of even small changes in the interest rate.

Consider the following loan. Complete parts (a)-(c) below. An individual borrowed $84,000 at an APR of 6%, which will be paid off with monthly payments of $541 for 25 years. a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount. The amount borrowed is $___, the annual interest rate is ___%, the number of payments per year is ___, the loan term is ___ years, and the payment amount is $___. b. How many total payments does the loan require? What is the total amount paid over the full term of the loan? There are ___ payments toward the loan and the total amount paid is $___. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest? The percentage paid toward the principal is ___% and the percentage paid for interest is ___%.

Explore the amortization of an $84,000 loan at 6% APR with $541 monthly payments over 25 years. Learn how to calculate the total number of payments, total amount paid, and the percentage of payment toward principal and interest. This guide covers key concepts in loan payments and interest calculation.

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