B1.4 Calculate total interest earned or paid | Ontario Grade 11 Mathematics

Ontario Grade 11 Mathematics

Personal Finance

Grade 11 MBF3C • Study guide label: B1.4

Interest is money paid for the use of money. A financial institution may pay interest when you save money. A lender may charge interest when you borrow money. This lesson focuses on calculating the total interest earned or paid using simple interest. Simple interest is calculated on the original amount only. It does not include interest added to the balance and then used to calculate more interest. The goal is to find the interest over the full time period, not just the interest for one year.

What you will learn

Identify the principal, annual interest rate, and time in a simple-interest problem.
Calculate the total interest earned on savings or paid on a loan.
Check that the time unit and interest-rate unit match.
Explain the difference between interest and the total amount of money.

1. Connect the parts of the problem

Before calculating interest, find three details in the question. The principal is the original amount saved or borrowed. The rate is the percent charged or earned each year. The time is how long the money is saved or borrowed. The interest rate is usually given as a percent per year.

For example, if a person borrows CAD 800 at an annual rate of 5% for 2 years, CAD 800 is the principal, 5% is the annual rate, and 2 years is the time. The word annual means per year. These details tell you what values belong in the simple-interest calculation.

A percent is a rate out of 100. To use a percent in a calculation, write it as a decimal: divide by 100. For example, 5% becomes 0.05. Keep the percent conversion clear so the answer is not 100 times too large.

Principal: the original amount saved or borrowed.
Annual rate: the interest rate for one year.
Time: the length of the saving or borrowing period.

2. Calculate simple interest

Simple interest means that each year’s interest is based on the original principal. The interest for one year is the principal multiplied by the annual rate written as a decimal. For more than one year, multiply that yearly interest by the number of years.

The formula brings these steps together. In the formula,

I

is the total interest,

P

is the principal,

r

is the annual rate written as a decimal, and

t

is the time in years. The formula works for both interest earned and interest paid. The situation tells you which one it is.

If the time is given in months, convert it to years before using the formula. For example, 6 months is half a year. This matters because the rate is per year. Using 6 as the time would incorrectly treat 6 months as 6 years.

I=Prt

Convert a percent rate to a decimal before substituting.
Use time in years when the rate is annual.
The result is the total interest for the full period.

3. Interpret and check the result

Interest and total amount are not the same. Interest is only the extra money earned or paid. The total amount is the principal plus the interest. If a question asks for total interest, report

I

, not the principal-plus-interest amount.

A quick reasonableness check can catch errors. For a period of one year, interest should be the principal multiplied by the decimal rate. For a longer period, simple interest increases in proportion to time. If a rate is 4% per year for 3 years, the total simple-interest rate over that period is 12% of the original principal.

Check the units and the context before finishing. A savings question asks how much interest is earned; a borrowing question asks how much interest is paid. If the answer is money, include the currency and round to the nearest cent when appropriate.

\text{total amount}=P+I

Interest is not the same as the final balance or repayment total.
Simple interest is based on the original principal for the whole period.
Check that the answer fits the rate, time, and situation.

4. Use the method in different situations

The same calculation applies whether the money is saved or borrowed. For savings, the result is interest earned. For a loan, it is interest paid. Read the wording carefully: a question may ask for interest alone, or it may ask for the total amount after interest is included.

A useful way to organize the work is to list the principal, rate, and time, convert the rate to a decimal, and then substitute. Keep the final answer tied to the question. This prevents mixing up the amount borrowed with the cost of borrowing.

Use the same simple-interest formula for earning and paying interest.
State whether the calculated interest is earned or paid.
Only add principal when the question asks for the total amount.

Worked example

Interest earned on savings

Mina deposits CAD 1,250 in an account that earns simple interest at 3.2% per year for 18 months. How much interest does she earn?

Identify the values
The principal is CAD 1,250 and the annual rate is 3.2%. Convert 18 months to years because the rate is given per year.
$t=18\div12=1.5$
Convert the rate
Write the percent as a decimal by dividing by 100. This gives the rate to use in the formula.
$r=3.2\div100=0.032$
Calculate the interest
Substitute the principal, decimal rate, and time. Multiplying by 1.5 accounts for one and a half years of interest on the original deposit.
$I=1250(0.032)(1.5)=60$

Answer: Mina earns CAD 60.00 in interest.

Check: One year of interest is CAD 40.00. For 1.5 years, CAD 40.00 multiplied by 1.5 is CAD 60.00, so the result is reasonable.

Worked example

Interest paid on a loan

A student borrows CAD 2,400 at a simple annual interest rate of 6.5% for 9 months. How much interest will the student pay?

Identify the values
The principal is CAD 2,400 and the annual rate is 6.5%. Convert 9 months into part of a year so the time unit matches the annual rate.
$t=9\div12=0.75$
Convert the rate
Divide 6.5 by 100 to express the annual rate as a decimal.
$r=6.5\div100=0.065$
Calculate the interest
Use the simple-interest formula with the original loan amount. The result is the cost of interest for the nine-month period, not the full amount to repay.
$I=2400(0.065)(0.75)=117$

Answer: The student will pay CAD 117.00 in interest.

Check: A full year of interest would be CAD 156.00. Nine months is three quarters of a year, and three quarters of CAD 156.00 is CAD 117.00.

Common mistakes and how to avoid them

Using 3.2 instead of 0.032 for a rate of 3.2%.

Correction: Convert the percent to a decimal by dividing by 100 before substituting.

Using the number of months directly as the time when the rate is annual.

Correction: Convert months to years by dividing the number of months by 12.

Reporting principal plus interest when asked for interest only.

Correction: Report the value of

I

for an interest question. Add principal only if the question asks for the total amount.

Calculating interest on a growing balance in a simple-interest question.

Correction: For simple interest, use the original principal for the full time period.

Lesson summary

Find the principal, annual rate, and time.
Convert the annual percent rate to a decimal and express time in years.
Calculate total simple interest using $I=Prt$ .
State whether the interest is earned or paid, and distinguish it from the total amount.

Check your understanding

Question 1

A deposit of CAD 900 earns simple interest at 4% per year for 2 years. How much interest is earned?

CAD 36.00
CAD 72.00
CAD 936.00
CAD 180.00

Show answer and explanation

CAD 72.00

Convert 4% to 0.04, then calculate

900(0.04)(2)=72

. The interest earned is CAD 72.00.

Question 2

A loan of CAD 1,500 has a simple annual interest rate of 8% for 6 months. What is the interest paid?

CAD 120.00
CAD 60.00
CAD 1,560.00
CAD 7.20

Show answer and explanation

CAD 60.00

Six months is 0.5 years and 8% is 0.08. The interest is

1500(0.08)(0.5)=60

, so the student pays CAD 60.00 in interest.

Key terms

Simple interest: Interest calculated on the original principal only.
Principal: The original amount saved or borrowed.
Annual rate: An interest rate stated for one year.
Interest: Money earned for saving or paid for borrowing.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MBF3C), expectation B1.4. It is a study resource, not an official curriculum publication.

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B1.4 · Calculate total interest earned or paid