B2.3 · Compare simple and compound interest

Ontario Grade 11 Mathematics

Saving, Investing, and Borrowing

MEL3E study topic: B2.3

What you will learn

• Explain how simple interest and compound interest are calculated over time.
• Use repeated calculations or a calculator to find a balance.
• Compare two interest options when the starting amount, rate, and time are the same.

Start with the same basic terms

• Principal means the starting amount.
• A rate of 4% means CAD 4 of interest for each CAD 100 for one year.
• Compare options using the same principal, rate, time, and calculation schedule.

Simple interest: use the starting amount each year

• Simple interest is calculated from the original principal each year.
• When the principal and rate do not change, the interest added each year stays the same.
• Keep the previous balance visible so each new year's balance is clear.

Compound interest: use the current balance

• Compound interest is calculated from the current balance at the start of each period.
• Each new balance becomes the amount used for the next period.
• The difference between the methods can grow over time.

Make a fair comparison

• Keep the starting amount, rate, and time the same in the comparison.
• A larger savings balance is generally better; a larger loan balance is generally worse.
• State whether the balance is money saved or money owed.

How the yearly calculation differs

Worked example

Compare savings over three years

1. Find the yearly simple interest
   For simple interest, use the original CAD 500 each year. Convert 4% to 0.04, then multiply. This gives the same interest amount in each of the three years.
   $$500 \times 0.04 = 20$$
2. Build the simple-interest balance
   Add CAD 20 to the balance at the end of each year. Repeating the addition gives the balance after year three.
   $$500 \rightarrow 520 \rightarrow 540 \rightarrow 560$$
3. Calculate the first compound year
   For compound interest, calculate the first year's interest from CAD 500. Add it to get the balance used at the start of year two.
   $$500 \times 0.04 = 20,\quad 500 + 20 = 520$$
4. Continue compounding
   Use CAD 520 for year two, then use the resulting balance for year three. Round each year's balance to the nearest cent.
   $$520 \times 0.04 = 20.80,\quad 520 + 20.80 = 540.80$$
5. Finish the comparison
   Calculate 4% of CAD 540.80 for year three, then compare the final compound balance with the simple-interest balance.
   $$540.80 \times 0.04 = 21.632,\quad 540.80 + 21.63 = 562.43$$

Worked example

Compare two borrowing costs

1. Calculate simple interest each year
   Simple interest uses the original CAD 1,200 for both years. Find 5% of that principal. The same amount is added in each year.
   $$1{,}200 \times 0.05 = 60$$
2. Find the simple-interest amount owed
   Add CAD 60 for each of two years to the amount borrowed. This gives the total owed under simple interest.
   $$1{,}200 + 60 + 60 = 1{,}320$$
3. Calculate the first compound year
   For the first year, 5% is calculated from CAD 1,200. Add that interest to find the amount used for the next year's calculation.
   $$1{,}200 \times 0.05 = 60,\quad 1{,}200 + 60 = 1{,}260$$
4. Calculate the second compound year
   The second year's interest is based on CAD 1,260, not the original CAD 1,200. Add the interest to find the final amount owed.
   $$1{,}260 \times 0.05 = 63,\quad 1{,}260 + 63 = 1{,}323$$

Common mistakes and how to avoid them

Lesson summary

• Simple interest is calculated from the original principal each year.
• Compound interest is calculated from the current balance at the start of each year.
• Use repeated calculations, a calculator, or a spreadsheet to find each new balance.
• Compare final balances under matching terms, and interpret the result based on whether the money is saved or borrowed.

Check your understanding

Key terms

Interest

Money paid for the use of money.

Principal

The starting amount saved or borrowed.

Balance

The amount in an account or the amount still owed at a particular time.

Simple interest

Interest calculated from the original principal each period.

Compound interest

Interest calculated from the current balance, which includes interest added earlier.

Continue through MEL3E

View the complete MEL3E Ontario Grade 11 Mathematics curriculum and lessons

• B2.2 · Calculate compound interest by repeated simple-interest steps
• B2.4 · Investigate how investment conditions affect future value
• B1.1 · Compare savings services, costs, and ways to reduce fees
• B1.2 · Compare credit-card and debit-card costs and incentives
• B1.3 · Read financial statements and use them to manage money
• B2.1 · Investigate and solve simple-interest problems

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation B2.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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