Simple interest | Year 9 | Ascent Library

01 / LEARN

Understand the idea.

Interest on the original principal

Simple interest is earned on the original principal throughout the term. In $I = P r t$ , use principal $P$ , annual decimal rate $r$ and time $t$ in years. The accumulated amount includes both principal and interest: $A = P + I$ .

With $800$ dollars at $4 %$ per year, each year earns $800 \times 0.04 = 32$ dollars. Three years earns three equal increments. Because earlier interest is not added to the interest-calculation base, this growth is linear.

Match units and isolate the unknown

Match the time unit to the rate. With an annual rate, convert months to years by dividing by $12$ : six months is $0.5$ years. Convert a percentage to a decimal before substituting it.

When a different quantity is unknown, rearrange the same formula rather than inventing a new rule. For example, dividing by $P t$ gives $r = \frac{I}{P t}$ . Report this decimal rate as a percentage and check it by substitution.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example

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

Worked solution

1
Record the compatible inputs.
$P = 800, r = \frac{4}{100} = 0.04, t = 3$
The rate is annual and the time is already measured in years.
2
Calculate the simple interest.
$I = 800 (0.04) (3) = 96 dollars$
The same principal earns interest for all three years.
3
Add the principal back.
$A = 800 + 96 = 896 dollars$
Interest is the increase; the final amount also includes the starting money.
4
Check the annual increments.
$800 (0.04) = 32, 3 (32) = 96$
Three identical annual interest amounts confirm the total interest.

Answer

Interest AUD 96.00; final amount AUD 896.00

EXAMPLE 02

Worked example

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

Worked solution

1
Substitute the known quantities.
$90 = 600 r (3)$
The given 90 dollars is interest, so it belongs on the left of I equal to Prt.
2
Divide by principal times years.
$r = \frac{90}{600 \times 3} = 0.05$
Dividing both sides by 1800 isolates the annual decimal rate.
3
Convert the rate to a percentage.
$0.05 \times 100 % = 5 % per year$
The decimal fraction must be expressed as a percentage for the requested rate.
4
Check the calculated rate.
$600 (0.05) (3) = 90 dollars$
The recovered rate reproduces the stated interest over three years.

Answer

5% per year

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

AUD 12.00

Use $r = 0.03$ and $t = 2$ : $I = 200 (0.03) (2) = 12$ dollars. This is the interest alone; adding the principal would give a final amount of $212$ dollars.

Keep practising

6 worksheet questions · 16 marks

Open worksheet 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
$P = \frac{72}{0.04 \times 3} = 600$ .
AUD 600.00
How many years does 400 dollars take to earn 80 dollars simple interest at 5% per year?
2 marks
$t = \frac{80}{400 \times 0.05} = 4$ .
$4$ years
A 700-dollar principal earns 63 dollars simple interest in 18 months. Find the annual rate.
3 marks
$t = 1.5$ .
$r = \frac{63}{700 \times 1.5} = 0.06 = 6 %$ .
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 ↗

In this lesson

Understand the idea.

Interest on the original principal

Match units and isolate the unknown

See the method in action.

Worked example

Record the compatible inputs.

Calculate the simple interest.

Add the principal back.

Check the annual increments.

Worked example

Substitute the known quantities.

Divide by principal times years.

Convert the rate to a percentage.

Check the calculated rate.

Try it yourself.

Check your understanding

Keep practising