Simple interest | Year 9 | Ascent Library

01 / LEARN

The idea, step by step

Interest on the original principal

Simple interest is calculated on the original principal throughout the term. In $I = P r t$ , $P$ is the starting amount, $r$ is the annual rate written as a decimal, and $t$ is the time in years. The final amount is $A = P + I$ .

If $P = 800$ , $r = 0.04$ and $t = 3$ , then $I = 96$ dollars and $A = 896$ dollars. The interest earned each year is the same 32 dollars. This is a linear growth model, not interest on previously earned interest.

Match units and isolate the unknown

For an annual rate, six months is $0.5$ years and eighteen months is $1.5$ years. Using 18 as the number of years would multiply the interest by 12. Read the period stated with the rate before substituting.

To find a missing principal, rate or term, rearrange the same formula. For example, $r = I / (P t)$ . Convert a decimal rate back to a percentage when reporting it. These examples are hypothetical and omit fees unless the question supplies them.

A common trap

Use 5 instead of 0.05 as the rate for 5%.

Instead: Convert percentage to decimal before multiplying; 5% is $5 / 100 = 0.05$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example

An account uses simple interest on 800 dollars at 4% per year for 3 years. Find the interest and final amount.

$I = 800 \times 0.04 \times 3 = 96$ .
$A = 800 + 96 = 896$ .
Annual interest is $800 \times 0.04 = 32$ dollars.

Interest AUD 96.00; final amount AUD 896.00

Example 2

Worked example

A principal of 600 dollars earns 90 dollars simple interest in 3 years. Find the annual rate.

$r = I / (P t) = 90 / (600 \times 3) = 0.05$ .
$0.05 = 5 %$ .
Check $600 \times 0.05 \times 3 = 90$ .

5% per year

Check your understanding

Find simple interest on 200 dollars at 3% per year for 2 years.

Show answer

AUD 12.00

$200 \times 0.03 \times 2 = 12$ .

03 / WORKSHEET

Your turn

6 questions · 16 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the interest and final amount for 1,200 dollars at 5% simple interest per year for 2 years.
3 marks
Find simple interest on 500 dollars at 6% per year for 6 months.
2 marks
At 4% simple interest per year for 3 years, an investment earns 72 dollars interest. Find the principal.
3 marks
How many years does 400 dollars take to earn 80 dollars simple interest at 5% per year?
2 marks
A 700-dollar principal earns 63 dollars simple interest in 18 months. Find the annual rate.
3 marks
Compare only the total interest: 800 dollars at 4% simple interest for 3 years, or at 5% for 2 years.
3 marks

Read the worked solutions

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

Find the interest and final amount for 1,200 dollars at 5% simple interest per year for 2 years.
3 marks
$I = 1200 (0.05) (2) = 120$ .
$A = 1200 + 120 = 1320$ .
Interest AUD 120.00; final AUD 1,320.00
Find simple interest on 500 dollars at 6% per year for 6 months.
2 marks
$t = 0.5$ years.
$I = 500 (0.06) (0.5) = 15$ .
AUD 15.00
At 4% simple interest per year for 3 years, an investment earns 72 dollars interest. Find the principal.
3 marks
$P = 72 / (0.04 \times 3) = 600$ .
AUD 600.00
How many years does 400 dollars take to earn 80 dollars simple interest at 5% per year?
2 marks
$t = 80 / (400 \times 0.05) = 4$ .
$4$ years
A 700-dollar principal earns 63 dollars simple interest in 18 months. Find the annual rate.
3 marks
$t = 1.5$ .
$r = 63 / (700 \times 1.5) = 0.06 = 6 %$ .
6% per year
Compare only the total interest: 800 dollars at 4% simple interest for 3 years, or at 5% for 2 years.
3 marks
$800 (0.04) (3) = 96$ and $800 (0.05) (2) = 80$ .
The terms differ, so this does not mean 4% is a higher annual rate.
The first earns AUD 96.00; the second AUD 80.00, so the first earns AUD 16.00 more.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 9 financial modelling within AC9M9A05 and AC9M9M05; supplied hypothetical rates and costs, not financial advice.

Official curriculum source ↗

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