Simple interest | Year 11 | Ascent Library

01 / LEARN

The idea, step by step

Identify principal and time

Simple interest is calculated only on the original principal. With principal $P$ , decimal annual rate $r$ and time $t$ in years, $I = P r t$ . The final balance is $A = P + I$ .

Convert months to years before using an annual rate. Nine months is 0.75 year. If days are used, the problem must specify a day-count convention, such as 365 days per year.

Find an unknown

Rearrange the same equation to find a principal, rate or time: $P = I / (r t)$ , $r = I / (P t)$ or $t = I / (P r)$ . Use the interest earned, not the final balance, for $I$ .

The balance grows by the same dollar amount each year, so a simple-interest graph is linear. Always check whether the question asks for interest only or the total balance.

A common trap

Use time 9 for 9 months with an annual rate.

Instead: Use 9/12 year so the rate and time refer to the same unit.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example

Find interest and final balance on AUD 3200 at 4.5% simple interest for 9 months.

t=9/12=0.75.
I=3200×0.045×0.75=108.
A=3200+108.

AUD 108 interest; AUD 3308 final

Example 2

Worked example

AUD 2500 earns AUD 300 simple interest in 3 years. Find the annual rate.

r=300/(2500×3)=0.04.
0.04=4%.

4% p.a.

Check your understanding

Find simple interest on AUD 1500 at 6% p.a. for 4 months.

Show answer

AUD 30.00

1500×0.06×4/12=30.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Interest on AUD 4800 at 3.5% simple interest for 2 years?
2 marks
Final amount on AUD 1800 at 5% simple interest for 18 months?
2 marks
Find the principal earning AUD 144 in 2 years at 4.5% simple interest.
2 marks
Time for AUD 2000 to earn AUD 350 at 7% simple interest?
2 marks
Annual simple rate when AUD 3600 earns AUD 81 in 9 months?
2 marks
Using 365 days/year, find interest on AUD 7300 at 5% for 40 days.
2 marks

Read the worked solutions

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

Interest on AUD 4800 at 3.5% simple interest for 2 years?
2 marks
4800×0.035×2=336.
AUD 336.00
Final amount on AUD 1800 at 5% simple interest for 18 months?
2 marks
I=1800×0.05×1.5=135.
A=1935.
AUD 1,935.00
Find the principal earning AUD 144 in 2 years at 4.5% simple interest.
2 marks
P=144/(0.045×2)=1600.
AUD 1,600.00
Time for AUD 2000 to earn AUD 350 at 7% simple interest?
2 marks
t=350/(2000×0.07)=2.5.
2.5 years
Annual simple rate when AUD 3600 earns AUD 81 in 9 months?
2 marks
r=81/(3600×0.75)=0.03.
3%
Using 365 days/year, find interest on AUD 7300 at 5% for 40 days.
2 marks
I=7300×0.05×40/365=40.
AUD 40.00

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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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