Consider the following loan. Complete parts​ (a)-(c) below.
An individual borrowed ​$82 comma 000 at an APR of 5​%, which will be paid off with monthly payments of ​$558 for 19 years.b. How many total payments does the loan​ require? What is the total amount paid over the full term of the​ loan?
There are

enter your response here payments toward the loan and the total amount paid is ​$

enter your response here.

Let's break down the problem.

### Step 1: Calculate the total number of payments.
- The loan is for 19 years.
- Payments are made monthly.

Total number of payments $ N $ is calculated by:
\[
N = \text{Number of years} \times \text{Number of months per year}
\]
\[
N = 19 \times 12 = 228 \text{ payments}
\]

### Step 2: Calculate the total amount paid over the full term of the loan.
- Each monthly payment is $558.
- The total amount paid $ T $ is calculated by:
\[
T = \text{Monthly payment} \times \text{Total number of payments}
\]
\[
T = 558 \times 228 = 127,224 \text{ dollars}
\]

### Final Answers:
- **Total number of payments**: 228 payments
- **Total amount paid**: $127,224

Would you like details on how to calculate the interest paid or have any other questions?

Here are five questions related to this problem:
1. How is the principal of the loan different from the total amount paid?
2. What does the APR represent in a loan?
3. How would the total amount paid change if the loan term were shorter?
4. What is the formula for calculating the monthly payment on a loan?
5. How much interest is paid over the life of the loan?

**Tip:** When calculating loan payments, always check if there are any additional fees or prepayment penalties that could affect the total cost.

Learn how to calculate the total number of payments and the total amount paid over the full term of a loan using monthly payments. This example problem involves an $82,000 loan at 5% APR with monthly payments of $558 for 19 years. Understand the formulas and steps needed for similar loan calculations.

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