B3.3 Calculate total interest over the life of a loan

Ontario Grade 11 Mathematics

Saving, Investing, and Borrowing

MEL3E • B3.3 • Use the loan’s payment record to calculate interest paid over its full term.

A loan lets someone use money now and repay it over time. The extra amount paid to borrow that money is called interest. To find the total interest over a loan’s life, first find how much will be paid altogether. Then subtract the amount originally borrowed. This lesson uses the payment amount and payment count shown in a loan record. It does not estimate a payment from a rate or other loan details.

What you will learn

Identify the amount borrowed, each payment, and the number of payments from a loan record.
Use a calculator or spreadsheet to add all payments over the loan’s life.
Calculate total interest by subtracting the amount borrowed from the total paid.

Start with the loan record

A loan record may show the amount borrowed, the regular payment, how often payments are made, and how many payments are required. The amount borrowed is the starting amount the borrower receives. A payment is an amount paid back to the lender.

For this calculation, use the stated payment amount and the total number of payments. Check that the payment count covers the whole loan. For example, a record might say there are 36 monthly payments. That means the same payment is made 36 times over the life of the loan.

The loan’s life means the full period from borrowing the money to making the last required payment. Total paid means the sum of all the payments over that period.

Find the amount borrowed and the payment count before calculating.
Use the payment schedule for the entire loan, not just one month or one year.

Find the total amount paid

When every payment is the same, add the payment once for each scheduled payment. A calculator can do this as multiplication: payment amount times number of payments. Multiplication is a quick way to add equal amounts repeatedly.

For example, 36 payments of CAD 180 give a total paid of CAD 6,480. This is the amount the borrower pays in all, not the interest alone.

If the payment record shows different payment amounts, add the listed payments instead. A spreadsheet can help: enter each payment in a cell and use the spreadsheet’s sum feature. Check that every payment is included once.

\text{Total paid}

=

\text{payment amount}

× number of payments

Equal payments: multiply one payment by the number of payments.
Different payments: add the payment amounts shown in the record.

Separate interest from borrowed money

The total paid includes two parts: the money borrowed and the interest. Once you know the total paid, subtract the original amount borrowed. The remainder is the total interest paid over the loan’s life.

For example, if a borrower receives CAD 5,000 and repays CAD 6,480 altogether, the difference is CAD 1,480. That difference is interest because it is the amount paid beyond the original loan amount.

Keep the units clear. The amount borrowed, total paid, and total interest should all be in the same currency. Do not subtract the payment amount from the amount borrowed; use the total of all payments.

\text{Total interest} = \text{total paid} - \text{amount borrowed}

Total interest is the total paid minus the amount borrowed.
A sensible result is a positive amount when the total paid is greater than the amount borrowed.

Use a calculator or spreadsheet carefully

A calculator is useful for multiplying a repeated payment and checking the subtraction. Enter the payment amount and payment count carefully, then compare the result with the loan record.

In a spreadsheet, you can enter the payment amount in one cell and the number of payments in another. A multiplication formula gives the total paid. Subtract the borrowed amount to get total interest. If actual payments vary, list them and add the full list before subtracting the amount borrowed.

Before accepting a result, ask: Did I use the full payment count? Did I include every payment? Did I subtract the amount borrowed from the total paid? These checks help catch common entry errors.

Technology helps with repeated calculations, but the loan details still need to be read correctly.
Round only if the payment record requires it; use the stated payment amounts as given.

Worked example

A used car loan

A loan record shows that a customer borrowed CAD 8,400 and must make 48 monthly payments of CAD 215. Calculate the total interest over the life of the loan.

Find the total paid
There are 48 equal payments. Multiply the amount of one payment by 48 to include every monthly payment.
$48 × 215 = 10{,}320$
Subtract the amount borrowed
The total paid contains the original CAD 8,400 as well as interest. Subtract the amount borrowed to find only the interest.
$10{,}320 - 8{,}400 = 1{,}920$

Answer: The total interest is CAD 1,920.

Check: The total paid, CAD 10,320, is greater than the CAD 8,400 borrowed. The difference is CAD 1,920.

Worked example

A laptop loan with weekly payments

A worker borrows CAD 2,750 for equipment. The agreement lists 52 weekly payments of CAD 62. Calculate the total interest over the life of the loan.

Calculate all payments
The agreement lists the same amount for each of 52 payments. Multiply CAD 62 by 52 to find the full amount paid.
$52 × 62 = 3{,}224$
Find the interest portion
Subtract the original amount borrowed from the total paid. The remaining amount is the cost of borrowing across the full loan.
$3{,}224 - 2{,}750 = 474$

Answer: The total interest is CAD 474.

Check: Adding CAD 474 interest to CAD 2,750 borrowed gives CAD 3,224, which matches the total of the 52 payments.

Common mistakes and how to avoid them

Reporting the total of all payments as the total interest.

Correction: Subtract the amount borrowed from the total paid. Only the difference is interest.

Multiplying by the number of years instead of the number of payments.

Correction: Use the payment count shown on the loan record. A weekly or monthly payment schedule may have many payments in one year.

Using only a few payments instead of the full schedule.

Correction: Check that the count or list includes every payment through the final payment.

Lesson summary

Read the amount borrowed, payment amount, and full payment count from the loan record.
Find total paid by multiplying equal payments by their count, or add payments that vary.
Subtract the amount borrowed from total paid to calculate total interest.
Use a calculator or spreadsheet to check arithmetic and confirm that all payments are included.

Check your understanding

Question 1

A loan is for CAD 3,600. The borrower makes 24 equal payments of CAD 170. What is the total interest?

CAD 480
CAD 4,080
CAD 3,600
CAD 170

Show answer and explanation

CAD 480

The total paid is 24 times CAD 170, or CAD 4,080. Subtract CAD 3,600 borrowed: the interest is CAD 480.

Question 2

A loan record lists 40 payments of CAD 95 and an amount borrowed of CAD 3,200. Which calculation finds the total interest?

CAD 95 minus CAD 3,200
40 times CAD 95, then subtract CAD 3,200
CAD 3,200 divided by 40
40 times CAD 3,200, then subtract CAD 95

Show answer and explanation

40 times CAD 95, then subtract CAD 3,200

First find the total of all 40 payments. Then subtract the amount borrowed. The total paid is CAD 3,800, so the interest is CAD 600.

Key terms

Amount borrowed: The original amount of money the lender gives the borrower.
Payment: An amount paid back to the lender according to the loan schedule.
Total paid: The sum of every payment made over the full loan.
Total interest: The amount paid beyond the original amount borrowed.
Loan’s life: The full period from receiving the loan to making the final required payment.

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View the complete Ontario Grade 11 Mathematics learning path

About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation B3.3. It is a study resource, not an official curriculum publication.

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B3.3 · Calculate total interest over the life of a loan