Math Problem Statement

Use the​ add-on method of calculating interest to find the total interest and the monthly payment.

Amount of Loan

Length of Loan

Interest Rate

​$41004100

44

years

4.64.6​%

Question content area bottom

Part 1

The total interest is

​(Round to the nearest cent as​ needed.)

Solution

To calculate the total interest using the add-on method, we use the following formula:

Total Interest=P×r×t\text{Total Interest} = P \times r \times t

Where:

  • PP is the principal (loan amount).
  • rr is the annual interest rate (as a decimal).
  • tt is the time of the loan in years.

Given:

  • P=4100P = 4100
  • r=4.6%=0.046r = 4.6\% = 0.046
  • t=4 yearst = 4 \text{ years}

Now, let's calculate the total interest.The total interest for the loan is $754.40.

Next, we will calculate the monthly payment using the add-on method. The formula for the monthly payment is:

Monthly Payment=P+Total Interestt×12\text{Monthly Payment} = \frac{P + \text{Total Interest}}{t \times 12}

Let's calculate it now.The monthly payment for the loan is $101.13.

Would you like more details on this calculation, or do you have any questions?

Here are 5 related questions to expand your understanding:

  1. What is the difference between the add-on method and simple interest method?
  2. How would the total interest change if the loan term was extended to 5 years?
  3. What happens to the monthly payment if the interest rate increases to 5%?
  4. How does compound interest compare to the add-on method for loan repayments?
  5. What are the advantages of paying off a loan early?

Tip: Always check if your loan allows for early repayment without penalties, as this can save you money on interest.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Add-on Method
Loan Repayment

Formulas

Total Interest = P × r × t
Monthly Payment = (P + Total Interest) / (t × 12)

Theorems

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Suitable Grade Level

Grades 10-12