Year 9 - Simple interest - Free practice

Year 9 Simple Interest Worksheets

I = PRT - the Year 9 financial maths foundation.

Quick answer

How do you calculate simple interest?

Simple interest is calculated using I = PRT, where P is the principal (amount borrowed or invested), R is the annual interest rate as a decimal, and T is the time in years. For example, investing $2000 at 5% per year for 3 years earns I = 2000 × 0.05 × 3 = $300 in interest.

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Worked examples

Year 9 simple interest: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Calculating simple interest
Mia invests $4500 at a simple interest rate of 6% per annum for 3 years. Calculate the interest she earns.
Show worked solution
Key idea: Simple interest is calculated using $I = PRT$ , where $P$ is the principal, $R$ is the annual interest rate as a decimal, and $T$ is the time in years.
1. Identify the values: $P = 4500$ , $R = 0.06$ , $T = 3$ .
2. Substitute into the formula:
  $I = PRT = 4500 \times 0.06 \times 3$
3. Calculate:
  $I = 4500 \times 0.18 = 810$
Answer: Mia earns $810 in interest.
Example 2 · Rearranging for the interest rate
Jake borrows $7200 and repays a total of $9576 after 4 years with simple interest. Find the annual interest rate as a percentage.
Show worked solution
Key idea: First find $I$ from the total amount using $I = \text{Total} - P$ , then rearrange $I = PRT$ to get $R = \dfrac{I}{PT}$ .
1. Find the interest earned:
  $I = 9576 - 7200 = 2376$
2. Write the rearranged formula:
  $R = \frac{I}{PT}$
3. Substitute $P = 7200$ , $T = 4$ :
  $R = \frac{2376}{7200 \times 4} = \frac{2376}{28800}$
4. Calculate and convert to a percentage:
  $R = 0.0825 = 8.25\%$
Answer: The annual interest rate is $8.25\%$ .
Example 3 · Comparing simple interest scenarios
Priya has $5000 to invest. Bank A offers a simple interest rate of 4.8% per annum for 5 years. Bank B offers a simple interest rate of 5.5% per annum for 4 years. Which bank gives Priya a greater total amount at the end of the investment period, and by how much?
Show worked solution
Key idea: Calculate the total amount $A = P + I = P + PRT$ for each bank, then compare.
1. Bank A: $P = 5000$ , $R = 0.048$ , $T = 5$ :
  $\begin{gathered}I_A = 5000 \times 0.048 \times 5 = 1200 \\ A_A = 5000 + 1200 = 6200\end{gathered}$
2. Bank B: $P = 5000$ , $R = 0.055$ , $T = 4$ :
  $\begin{gathered}I_B = 5000 \times 0.055 \times 4 = 1100 \\ A_B = 5000 + 1100 = 6100\end{gathered}$
3. Compare:
  $A_A - A_B = 6200 - 6100 = 100$
Answer: Bank A gives a greater total amount by $100.

Common mistakes

Where students usually lose marks

Using the rate as a percentage instead of a decimal

I = 4500 × 6 × 3 = 81000

Always convert the percentage rate to a decimal before substituting into $I = PRT$ . Divide the percentage by 100, so $6\% = 0.06$ .

Forgetting to add principal to find the total amount

Total amount = I = $810, so Mia has $810 at the end.

$I$ is only the interest earned, not the final balance. The total amount is $A = P + I$ , so always add the original principal back.

Using months instead of years (or vice versa) for time

For an 18-month loan: T = 18 when the rate is per annum.

The time $T$ must match the period of the rate $R$ . If $R$ is an annual rate, convert months to years by dividing by 12. So 18 months $= 1.5$ years.

Rearranging the formula incorrectly

To find P: P = I - RT

Use inverse operations carefully. Starting from $I = PRT$ , divide both sides by $RT$ to get $P = \dfrac{I}{RT}$ . Writing the formula out before substituting helps avoid errors.

Try one yourself

Your turn

Anika invests $4500 at a simple interest rate of $6\%$ per year for $4$ years. What is the total amount, in dollars, in her account at the end of the $4$ years?

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About this worksheet

Why we built it

Year 9 students should be comfortable with the simple interest formula in both directions - finding the interest, and rearranging for principal, rate or time. These worksheets give your student a steady set of applied problems across each variation.

What's covered

Sub-skills your student will practise

✓Calculating simple interest using I = PRT
✓Rearranging for principal, rate or time
✓Converting between annual and monthly rates
✓Total amount = P + I problems
✓Comparing simple interest scenarios

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Frequently asked

Questions parents ask about simple interest

What's simple interest?

Interest calculated only on the original principal, not on accumulated interest. Formula: I = PRT, where P is the principal, R is the rate per year, and T is the time in years.

How does simple interest differ from compound interest?

Simple interest grows linearly (same dollar amount each year). Compound interest grows exponentially (each year's interest earns interest in subsequent years). Year 10 covers compound; Year 9 stays with simple.

How is the rate expressed in the formula?

As a decimal, not a percentage. A 5% rate becomes 0.05 in the formula. Forgetting to convert is the most common Year 9 simple-interest error.

Do students need to rearrange the formula?

Yes. Given any three of the four variables, students should be able to solve for the fourth. So 'find the principal needed to earn $500 interest at 4% over 2 years' is a standard Year 9 question.

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