Compound interest and compounding periods | Year 11

01 / LEARN

The idea, step by step

Compound growth

Compound interest becomes part of the next interest calculation. If the periodic decimal rate is $i$ , the balance is multiplied by $1 + i$ each period, giving $A = P {(1 + i)}^{n}$ .

For nominal annual rate $r$ with $m$ compounding periods per year, use $i = r / m$ and $n = m t$ . Dividing the rate and multiplying the period count are both required.

State the assumptions

The basic model assumes a constant rate and no added deposits, withdrawals or fees. When any of these occur, update the balance at the specified dates instead of treating the investment as a single uninterrupted sum.

Retain full calculator precision until the final answer unless a question specifies that interest is rounded at each credit. In a spreadsheet, each new balance is based on the preceding balance.

A common trap

Apply the annual rate every month.

Instead: A nominal annual rate must be divided by 12 when monthly periods are used.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example

Find the balance on AUD 2500 at 6% compounded annually for 3 years.

i=0.06;n=3.
A=2500(1.06)^3=2977.54.

AUD 2,977.54

Example 2

Worked example

Find the balance on AUD 4000 at 4.8% nominal p.a., compounded monthly for 2 years.

i=0.048/12=0.004;n=24.
A=4000(1.004)^24=AUD 4,402.19.

AUD 4,402.19

Check your understanding

At 6% nominal compounded quarterly for 3 years, what are i and n?

Show answer

i=0.015;n=12

i=0.06/4;n=4×3.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Balance on AUD 1000 at 5% compounded annually for 2 years?
2 marks
Compound interest on AUD 6000 at 4% annually for 3 years?
2 marks
Balance on AUD 1500 at 8% nominal compounded half-yearly for 2 years?
2 marks
Balance on AUD 8000 at 6% nominal compounded quarterly for 18 months?
2 marks
Compare AUD 2000 at 10% simple and 10% annual compound interest after 2 years.
2 marks
A monthly model uses B_next=1.005 B. State monthly and nominal annual rates.
2 marks

Read the worked solutions

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

Balance on AUD 1000 at 5% compounded annually for 2 years?
2 marks
A=1000(1.05)^2=1102.50.
AUD 1,102.50
Compound interest on AUD 6000 at 4% annually for 3 years?
2 marks
A=6000(1.04)^3=6749.184.
Interest=A−6000.
AUD 749.18
Balance on AUD 1500 at 8% nominal compounded half-yearly for 2 years?
2 marks
i=0.04;n=4.
A=1500(1.04)^4.
AUD 1,754.79
Balance on AUD 8000 at 6% nominal compounded quarterly for 18 months?
2 marks
i=0.015;n=6.
A=8000(1.015)^6.
AUD 8,747.55
Compare AUD 2000 at 10% simple and 10% annual compound interest after 2 years.
2 marks
Simple=2000(1+0.1×2).
Compound=2000(1.1)^2.
AUD 2400 simple; AUD 2420 compound
A monthly model uses B_next=1.005 B. State monthly and nominal annual rates.
2 marks
i=0.005.
12 i=0.06.
0.5% monthly;6% nominal p.a.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics: investing and borrowing. Supplied educational models cover interest, investment comparisons, shares and credit; they are not recommendations of real products or statements of personal tax liability.

Official curriculum source ↗

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