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F1.4 · Compare simple and compound interest with digital tools

Learn to compare simple and compound interest with digital tools through clear examples and targeted practice.

Ontario Grade 8 Mathematics

Financial Literacy

Use a digital tool to compare how savings can grow

Interest is money added to savings, or money charged for borrowing. In this lesson, we compare two ways that interest on savings can be calculated. Simple interest is based on the starting amount. Compound interest is based on the amount after earlier interest has been added. We will use hypothetical examples and a spreadsheet-style table. The examples are for learning, not current financial offers.

What you will learn

  • Explain the difference between simple and compound interest.
  • Use a digital tool, such as a spreadsheet, to calculate and compare interest.
  • Describe how the time period affects the difference between the two models.

Start with a concrete comparison

Imagine saving CAD 200 at a hypothetical yearly interest rate of 5% for three years. The starting amount is called the principal. A rate of 5% means 5 out of every 100, or CAD 0.05, for each CAD 1 in the amount being used to calculate interest.
With simple interest, the same interest is added each year. Five percent of CAD 200 is CAD 10, so the balance increases by CAD 10 each year. After three years, the total is CAD 230.
With compound interest, each year's interest is added to the balance. The next year's interest is calculated using this new balance. So the interest can grow from year to year.
5%=0.055\%=0.05
  • The principal is the starting amount saved or borrowed.
  • A yearly rate tells what fraction of the calculation amount is added each year.
  • Simple interest uses the principal each year; compound interest uses the updated balance.

Organize the comparison in a digital tool

A spreadsheet can calculate both balances year by year. Make columns for the year, the simple-interest balance, and the compound-interest balance. Enter the principal as the balance at year zero.
For the simple-interest column, add the same interest amount each year. For the compound-interest column, find the rate of the previous balance and add it to that balance. A spreadsheet can repeat each calculation in the next row. Check that the first row after year zero matches your hand calculation.
The table below shows the hypothetical CAD 200 example. The compound balance is rounded to the nearest cent for display. Keeping extra decimal places during calculations can prevent small rounding differences.
new compound balance=previous balance+0.05×previous balance\text{new compound balance}=\text{previous balance}+0.05\times\text{previous balance}
  • Use the same principal, rate, and number of years in both columns.
  • A spreadsheet makes repeated yearly calculations easier to compare.
  • Rounding is for displaying money; use the same rounding approach for both results.

Read the results and compare fairly

At the end of year one, both balances are CAD 210. The first year's interest is calculated from the same starting principal in both models.
In later years, the compound balance becomes larger in this example. That happens because the interest added in an earlier year is included in the balance used for the next year's calculation. Simple interest continues to add CAD 10 each year.
A fair comparison keeps the principal, yearly rate, and time period the same. If any of these changes between the two calculations, the difference may not be caused only by the interest method.
difference=compound balance−simple balance\text{difference}=\text{compound balance}-\text{simple balance}
  • Compare matching time periods and matching starting conditions.
  • The difference between the balances can become larger over time.
  • A higher ending balance in a hypothetical example is not a promise about a real account.

Use digital results thoughtfully

A digital tool follows the values and instructions entered by its user. Check the rate, principal, and number of years before trusting its output. Make sure the rate is entered as a percent or decimal in the way the tool expects.
For a spreadsheet, write down what each column means. Then compare a result from the tool with a small hand calculation, such as the first year's interest. This is a useful check for a misplaced cell reference or a rate entered incorrectly.
When you discuss the results, state the conditions. For example, say that one balance is larger after three years at the same hypothetical rate. Do not claim that every compound-interest result is better in every real situation; this lesson compares the two calculation methods under the same savings conditions.
  • Check the inputs and the meaning of each column.
  • Verify at least one digital result with a simple calculation.
  • Describe the comparison using its stated hypothetical conditions.

Year-by-year balances for the CAD 200 example

YearSimple interest balance (CAD)Compound interest balance (CAD)
0200.00200.00
1210.00210.00
2220.00220.50
3230.00231.53

Worked example

Compare balances over three years

A hypothetical savings amount of CAD 200 earns 5% per year for three years. Compare simple and compound interest using a year-by-year table.
Balances after three years
Balances after three yearsHypothetical CAD 200 savings amount at 5% per year. The two bars use the same conditions.230 CADSimple231.53 CADCompound

Hypothetical CAD 200 savings amount at 5% per year. The two bars use the same conditions.

  1. Find the simple-interest increase
    Five percent of the starting CAD 200 is CAD 10. Simple interest adds that same amount each year.
    200×0.05=10200\times0.05=10
  2. Calculate the simple balance
    Add CAD 10 in each of the three years. The balance reaches CAD 230.
    200+3×10=230200+3\times10=230
  3. Calculate the compound balance
    For each year, add 5% of the previous year's balance. Round the final displayed amount to the nearest cent.
    200×1.05×1.05×1.05=231.525200\times1.05\times1.05\times1.05=231.525
  4. Compare
    After three years, compound interest gives CAD 1.53 more than simple interest in this hypothetical example.
    231.53−230=1.53231.53-230=1.53
Answer: The simple-interest balance is CAD 230.00. The compound-interest balance is CAD 231.53 when rounded to the nearest cent.
Check: The simple balance increases by CAD 10 each year. The compound balance increases by CAD 10.00, then CAD 10.50, then CAD 11.03 when rounded to cents.

Worked example

Notice what changes after year one

A hypothetical CAD 100 earns 10% per year. Compare the two balances after two years.
Balances after two years
Balances after two yearsHypothetical CAD 100 savings amount at 10% per year.120 CADSimple121 CADCompound

Hypothetical CAD 100 savings amount at 10% per year.

  1. Find the first year's interest
    Both methods use the same starting amount in year one, so both add CAD 10.
    100×0.10=10100\times0.10=10
  2. Continue with simple interest
    Simple interest adds another CAD 10 in the second year.
    100+10+10=120100+10+10=120
  3. Continue with compound interest
    The compound balance after year one is CAD 110. The second year's interest is 10% of CAD 110, or CAD 11.
    110+110×0.10=121110+110\times0.10=121
Answer: After two years, the simple-interest balance is CAD 120 and the compound-interest balance is CAD 121.
Check: The balances match after year one. The compound balance is CAD 1 higher after year two because its second-year calculation uses CAD 110.

Worked example

Check a spreadsheet comparison

A spreadsheet compares hypothetical simple and compound interest on CAD 300 at 4% per year for two years. Decide whether the displayed results are consistent.
Balances after two years
Balances after two yearsHypothetical CAD 300 savings amount at 4% per year.324 CADSimple324.48 CADCompound

Hypothetical CAD 300 savings amount at 4% per year.

  1. Check the simple-interest result
    Four percent of CAD 300 is CAD 12 per year. Two equal yearly increases give a balance of CAD 324.
    300+2×12=324300+2\times12=324
  2. Check the compound result
    The first year's balance is CAD 312. Four percent of that is CAD 12.48, so the second year's balance is CAD 324.48.
    312+312×0.04=324.48312+312\times0.04=324.48
  3. Judge the display
    If the spreadsheet shows CAD 324 for simple interest and CAD 324.48 for compound interest, its results match the stated conditions. If it shows the same balance for both, check whether the compound calculation used the updated balance.
    324.48−324=0.48324.48-324=0.48
Answer: The consistent results are CAD 324.00 for simple interest and CAD 324.48 for compound interest.
Check: The compound result is CAD 0.48 higher. The second year's compound interest is based on CAD 312, not the original CAD 300.

Common mistakes and how to avoid them

Using the updated balance to calculate simple interest.
Correction: For simple interest, use the principal to find the same yearly interest amount each year.
Using the principal every year for compound interest.
Correction: For compound interest, use the balance from the previous year, including interest already added.
Comparing different rates or different time periods.
Correction: Keep the principal, rate, and number of years the same when comparing the two methods.
Rounding every value too early.
Correction: Keep extra decimal places in the digital calculation when possible, and round the displayed money amounts consistently.

Lesson summary

  • Simple interest adds the same amount each year because its calculation is based on the principal.
  • Compound interest adds interest based on the updated balance.
  • A spreadsheet can repeat yearly calculations and show the balances side by side.
  • Check that both methods use the same hypothetical principal, rate, and time period.

Check your understanding

Question 1

A hypothetical CAD 80 earns 5% per year. What is the simple-interest increase each year?
  1. CAD 4
  2. CAD 5
  3. CAD 8
  4. CAD 84
Show answer and explanation
CAD 4
Five percent of CAD 80 is CAD 4. Simple interest adds that amount each year.

Question 2

A compound-interest balance is CAD 210 at the end of one year. The hypothetical rate is 5%. Which amount should be used to find the next year's interest?
  1. The original principal only
  2. CAD 210
  3. The interest from year one only
  4. The number of years
Show answer and explanation
CAD 210
Compound interest uses the updated balance, which is CAD 210, for the next year's calculation.

Question 3

What should stay the same for a fair digital comparison of simple and compound interest?
  1. Only the colour of the spreadsheet cells
  2. The principal, rate, and time period
  3. The final balances
  4. The yearly interest amounts
Show answer and explanation
The principal, rate, and time period
Using the same principal, rate, and time period helps isolate the difference between the two interest methods.

Key terms

Interest
Money added to savings or charged for borrowing.
Principal
The starting amount of money saved or borrowed.
Rate
A fraction or percent used to calculate interest.
Simple interest
Interest calculated from the principal, giving the same interest amount each year when the rate is unchanged.
Compound interest
Interest calculated from the balance after earlier interest has been added.
Balance
The amount of money in the savings calculation at a particular time.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation F1.4. It is a study resource, not an official curriculum publication.

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