Math Problem Statement

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.

Solution

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 NN is calculated by: N=Number of years×Number of months per yearN = \text{Number of years} \times \text{Number of months per year} N=19×12=228 paymentsN = 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 TT is calculated by: T=Monthly payment×Total number of paymentsT = \text{Monthly payment} \times \text{Total number of payments} T=558×228=127,224 dollarsT = 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.

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Math Problem Analysis

Mathematical Concepts

Interest Calculation
Loan Payment Calculation

Formulas

Monthly payment calculation
Total payments calculation

Theorems

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Suitable Grade Level

High School