Math Problem Statement

Use the add-on method of calculating interest to find the total interest and the monthly payment for a $4400 loan over 5 years at an interest rate of 4.8%.

Solution

To calculate the total interest and monthly payment using the add-on method, we follow these steps:

Given:

  • Amount of loan (PP): $4400
  • Length of loan (tt): 5 years
  • Interest rate (rr): 4.8% (0.048 as a decimal)

Step 1: Total Interest

The formula for total interest in the add-on method is:

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

Substituting the values: Total Interest=4400×0.048×5\text{Total Interest} = 4400 \times 0.048 \times 5 Total Interest=1056\text{Total Interest} = 1056

Step 2: Total Amount to Repay

The total amount to repay is the principal (PP) plus the total interest:

Total Amount to Repay=P+Total Interest\text{Total Amount to Repay} = P + \text{Total Interest} Total Amount to Repay=4400+1056=5456\text{Total Amount to Repay} = 4400 + 1056 = 5456

Step 3: Monthly Payment

The monthly payment is calculated by dividing the total amount to repay by the total number of months:

Monthly Payment=Total Amount to RepayTotal Months\text{Monthly Payment} = \frac{\text{Total Amount to Repay}}{\text{Total Months}} Since the loan term is 5 years, the total months are: Total Months=5×12=60\text{Total Months} = 5 \times 12 = 60

Now: Monthly Payment=545660=90.93\text{Monthly Payment} = \frac{5456}{60} = 90.93

Final Answers:

  • Total Interest: $1056
  • Monthly Payment: $90.93

Would you like additional details or calculations?


Here are 5 related questions to expand your understanding:

  1. How does the add-on method differ from simple interest in terms of monthly payments?
  2. What would the monthly payment be for a shorter loan term, say 3 years?
  3. How would a higher interest rate (e.g., 6%) impact the total interest and monthly payment?
  4. Can this method be applied to other types of loans, such as mortgages?
  5. How can a borrower minimize their total interest when using the add-on method?

Tip: Always consider the total cost of the loan (interest + principal) when comparing loan offers, not just the monthly payment.

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Add-On Method
Monthly Payments

Formulas

Total Interest = Principal × Rate × Time
Total Repayment = Principal + Total Interest
Monthly Payment = Total Repayment ÷ Total Months

Theorems

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Suitable Grade Level

Grades 9-12