Simple versus compound growth | Year 10

01 / LEARN

The idea, step by step

Which amount earns interest?

In simple interest, each period uses the original principal $P$ . For annual decimal rate $r$ over $n$ years, $A = P (1 + r n)$ , so the increase is constant.

With annual compounding, the next interest calculation uses the current balance. The model $A = P {(1 + r)}^{n}$ has a constant percentage change but a changing amount of interest.

Use matching assumptions

Compare the same initial balance, rate convention and duration. Interest timing, deposits, withdrawals, fees and tax can change the result.

These are supplied classroom models rather than real account quotations. State the assumptions and separate final balance from interest earned.

A common trap

A 10% rate always means adding 10 dollars.

Instead: The percentage acts on a specified amount. Ten percent of 1000 dollars is 100 dollars; the base can change under compounding.

02 / WORKED EXAMPLES

See the thinking

Example 1

Three-year comparison

Compare 1000 dollars at 10% annually for 3 years using simple and annual compound interest.

Simple: $1000 (1 + 0.10 \times 3) = 1300$ .
Compound: $1000 {(1.10)}^{3} = 1331$ .
Compounding gives 31 dollars more because earlier interest also earns interest.

1300 dollars simple; 1331 dollars compound.

Example 2

Recognise a pattern

A balance is 500, 525 and 551.25 dollars at years 0, 1 and 2. Is it consistent with adding 25 annually or multiplying by 1.05?

The increases are 25 and 26.25, not constant.
Both consecutive ratios are $1.05$ .

Multiplication by 1.05.

Check your understanding

Find the yearly simple interest on 200 dollars at 5%.

Show answer

10 dollars

$200 \times 0.05 = 10$ each year.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the yearly simple interest on 800 dollars at 6%.
2 marks
Find the total after 4 years on 800 dollars at 6% simple interest.
2 marks
Find the total after 2 years on 800 dollars at 6% annual compound interest.
2 marks
Balances are 1000, 1040, 1080 at consecutive years. Identify the simple model rate.
2 marks
Compare simple and annual compound totals for 500 dollars at 10% annually for 2 years.
3 marks
Why do the two models agree after exactly one year when principal and annual rate match?
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the yearly simple interest on 800 dollars at 6%.
2 marks
$800 \times 0.06 = 48$ .
48 dollars
Find the total after 4 years on 800 dollars at 6% simple interest.
2 marks
$800 (1 + 0.06 \times 4) = 992$ .
992 dollars
Find the total after 2 years on 800 dollars at 6% annual compound interest.
2 marks
$800 {(1.06)}^{2} = 898.88$ .
898.88 dollars
Balances are 1000, 1040, 1080 at consecutive years. Identify the simple model rate.
2 marks
The yearly increase is 40, and $40 / 1000 = 0.04$ .
4% annually
Compare simple and annual compound totals for 500 dollars at 10% annually for 2 years.
3 marks
Simple: $500 (1 + 0.1 \times 2) = 600$ . Compound: $500 {(1.1)}^{2} = 605$ .
600 dollars simple; 605 dollars compound.
Why do the two models agree after exactly one year when principal and annual rate match?
3 marks
At $n = 1$ , both formulas equal $P (1 + r)$ .
Both apply the rate once to the original principal.

Checking saved progress…

Continue learning

Compound interest

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Simple versus compound growth; compound interest; depreciation; repeated percentage change; savings/loan scenarios with supplied models; changing assumptions and checking results; spreadsheets/digital models.

Official curriculum source ↗

Back to Financial mathematics