Calculate total interest paid on a loan

This skill involves determining the cumulative cost of borrowing by finding the interest portion of each payment on a fixed-rate loan, or by subtracting the original principal from the total of all scheduled repayments. It requires interpreting how principal, interest rate, loan term, payment frequency, and outstanding balance affect total interest, while distinguishing interest from the amount borrowed; fees, variable-rate loans, refinancing, and unusual repayment arrangements are excluded.

Detailed Explanation: Calculate total interest paid on a loan

To find the total interest paid on a fixed-rate loan:

Find the total number of payments.
Multiply the payment amount by the number of payments.
Subtract the original principal (the amount borrowed).

\text{Total interest} = \text{Total repayments} - \text{Original principal}

Worked example

A borrower takes out a loan of 10{,}000 $. The loan has a fixed interest rate of$ 6% $per year and is repaid with monthly payments of$ $443.21$ for 2 years. Find the total interest paid.

Step 1: Find the number of payments

There are 12 monthly payments each year:

2 \times 12 = 24 \text{ payments}

Step 2: Find the total amount repaid

24 \times \$443.21 = \$10{,}637.04

This is the total of all the payments, including both principal and interest.

Step 3: Subtract the original loan amount

\text{Total interest} = \$10{,}637.04-\$10{,}000

\boxed{\text{Total interest}=\$637.04}

The borrower pays 637.04 $in interest over the 2-year loan. The remaining$ $10{,}000$ of the repayments pays back the amount originally borrowed.

Learn by doing: Calculate total interest paid on a loan

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Financial Literacy - Interest and Fees - Simple - Interest Plus Fee to Total Payments

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