Simple Interest Explorer
Change the values and see the formula, working and graph update. You can find the interest, principal, rate, time or total amount.
Answer
How it works
See how the money grows
The graph updates after each calculation.
Enter your values and press Calculate to see how simple interest grows over time.
Simple Interest Practice Test
Build confidence from Year 9 foundations to Year 12 HSC Standard applications. Practise simple interest, total amount, time conversions, rearranging the formula, daily rates, linear models and multi-step financial problems.
- 8 progressive levels
- 50 practice questions
- Instant answer checks
- Hints and full working
Your answers and checked results are saved automatically in this browser.
Level 1
Simple Interest Basics
0/10
Level 2
Total Amount and Time Conversions
0/10
Level 3
Rearranging the Simple Interest Formula
0/5
Level 4
Simple Interest Word Problems
0/5
Level 5
Daily Rates and Mixed Time Periods
0/5
Level 6
Simple Interest Graphs and Linear Models
0/5
Level 7
HSC Standard Financial Applications
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Level 8
HSC Standard Challenge Problems
0/5
Simple interest is an important financial mathematics skill from the junior years through to HSC Mathematics Standard. The aim is not just to memorise one formula. You should be able to identify the principal, rate and time, rearrange the formula, convert time units and explain what your answer means.
What level should I practise?
Focus on the formula, simple interest, total amount and converting months to years.
Build confidence with rearranging formulas, financial applications, rates, units and linear relationships.
Practise investment, interest, loans, credit-card situations and making decisions from financial information.
Practise multi-step financial modelling, comparisons, borrowing, investments and interpreting results.
If percentages are still difficult, revise how to calculate percentages first. For broader Stage 5 revision, use the Year 9 NSW Maths guide or the Year 10 NSW Maths guide.
Simple Interest Formula
Simple interest is calculated on the original principal. If the principal and rate stay the same, the same amount of interest is added during each equal time period.
| Symbol | Meaning | Example |
|---|---|---|
| SI | Simple interest earned or charged | $300 |
| P | Principal — the original amount invested or borrowed | $2,000 |
| R | Interest rate per year | 5% means use R = 5 |
| T | Time in years when the rate is per annum | 3 years |
The official NSW Mathematics K–10 glossary also defines simple interest using the principal, rate and number of time periods.
How to Calculate Simple Interest
Example: $2,000 is invested at 5% p.a. for 3 years. Find the simple interest.
Step 1: Identify the values.
Step 2: Substitute into the formula.
Step 3: Calculate.
Answer: The simple interest is $300.
Interest is not always the final amount
If the question asks for the total amount, add the interest to the original principal.
In the example above, the total amount is $2,000 + $300 = $2,300.
How to Find the Principal, Rate or Time
In harder questions, the simple interest may already be given and another value is missing. Rearranging the formula first usually makes the working clearer. If algebraic rearranging is unfamiliar, revise Algebra Made Easy.
| Find | Formula |
|---|---|
| Simple Interest | SI = (P × R × T) ÷ 100 |
| Principal | P = (SI × 100) ÷ (R × T) |
| Rate | R = (SI × 100) ÷ (P × T) |
| Time | T = (SI × 100) ÷ (P × R) |
Example: Find the interest rate.
Dana invests $2,000 and earns $400 simple interest over 4 years. Find the annual interest rate.
Answer: 5% p.a.
Example: Find the principal.
An investment earns $360 at 6% p.a. simple interest over 3 years. Find the original principal.
Answer: The principal is $2,000.
Simple Interest With Months and Days
The rate and the time must refer to the same time period. If the rate is per annum, time should normally be written in years before you substitute into the formula.
| Given time | Convert to years |
|---|---|
| 3 months | 3 ÷ 12 = 0.25 years |
| 6 months | 6 ÷ 12 = 0.5 years |
| 9 months | 9 ÷ 12 = 0.75 years |
| 18 months | 18 ÷ 12 = 1.5 years |
Example: Interest for 9 months.
$4,000 is invested at 6% p.a. simple interest for 9 months.
Answer: $180 simple interest.
What if the rate is given per day?
If a question gives a daily rate, the number of days can be used directly because the units already match. For example, a debt of $1,800 charged at 0.05% per day for 30 days gives:
Senior students can explore official examples in the NSW Department of Education's Year 11 Mathematics Standard financial mathematics resources.
What Does a Simple Interest Graph Show?
Simple interest creates a straight-line relationship when the principal and rate remain constant. This happens because the same amount of interest is added during every equal time period.
Example: $2,000 at 5% p.a.
In A = 2000 + 100t, the value $2,000 is the starting amount and $100 is the increase each year. On a graph, $100 is the gradient. This links simple interest to linear relationships.
If gradient or straight-line equations need revision, use our Number Plane and Straight Lines guide. You can also use the interactive graph in the Simple Interest Explorer above.
Simple Interest for HSC Mathematics Standard 1 and Standard 2
Simple interest is not only a Year 9 topic. In senior Mathematics Standard, students use financial mathematics to solve practical problems and make decisions about investments, loans and borrowing.
Financial mathematics includes investment, depreciation and loans. Students need to select formulas, calculate accurately and interpret the result.
Financial mathematics extends into investment and loans, annuities and more detailed financial modelling and comparisons.
Under the NSW Mathematics Standard 11–12 Syllabus (2024), Standard 1 includes solving problems involving simple and compound interest to make decisions about financial situations, while Standard 2 includes modelling financial situations involving interest, depreciation and borrowing money. See the official Mathematics Standard outcomes and course structure.
What changes in an HSC-style question?
The arithmetic may still be simple, but the question often requires more than direct substitution. You may need to:
- decide which values represent principal, interest, rate and time
- convert months, days or rates into matching units
- find a missing value by rearranging a formula
- calculate a final balance rather than only the interest
- compare two financial options
- explain which option is better and why
- interpret a table, graph or spreadsheet result
For additional official senior resources, see the NSW Department of Education pages for Year 12 Mathematics Standard 1 financial mathematics and Year 12 Mathematics Standard 2 financial mathematics.
Common Simple Interest Mistakes
For SI = PRT ÷ 100, use R = 5 for 5%. If you use I = Prt, use r = 0.05.
If the rate is per annum, 6 months should usually be written as 6/12 = 0.5 years.
SI is only the interest. If the question asks for the final amount, use A = P + SI.
The principal is the original amount invested or borrowed, not the final balance.
Money answers need dollars, rate answers need %, and time answers need a unit such as years or months.
Simple Interest vs Compound Interest
The main difference is what the interest is calculated on. With simple interest, interest is calculated on the original principal. With compound interest, interest is added to the balance and future interest can then be calculated on that larger amount.
| Simple Interest | Compound Interest | |
|---|---|---|
| Interest calculated on | Original principal | Growing balance |
| Typical growth | Linear | Exponential |
| Graph | Straight line | Curved growth |
| Common formula | SI = PRT ÷ 100 | A = P(1 + r)n |
HSC-style comparison: $10,000 at 5% p.a. for 3 years.
Simple interest:
Compound interest, compounded annually:
The compound-interest investment gives $76.25 more after 3 years.
NSW Student Study Pathway
Simple interest connects to several other topics. If a question feels difficult, the problem may actually be a missing skill in percentages, algebra, rates or linear relationships.
Go directly to the 50-question Simple Interest Practice Test. Start with the easier levels and move towards Year 11 and HSC Standard questions.
Simple Interest FAQs
What is simple interest in one sentence?
Simple interest is interest calculated on the original principal rather than on previously earned interest.
What is the simple interest formula?
When the rate is entered as a percentage, use SI = (P × R × T) ÷ 100.
How do I find the total amount?
Calculate the simple interest first, then use A = P + SI.
How do I use 5% in the formula?
For SI = PRT ÷ 100, use R = 5. For I = Prt, use r = 0.05.
How do I calculate simple interest for 6 months?
If the rate is per annum, convert the time to years: 6 ÷ 12 = 0.5 years.
How do I find the interest rate?
Rearrange the formula to R = (SI × 100) ÷ (P × T).
How do I find the principal?
Use P = (SI × 100) ÷ (R × T).
How do I find the time?
Use T = (SI × 100) ÷ (P × R).
Why is the simple-interest graph a straight line?
Because the same amount of interest is added in each equal time period when the principal and rate remain constant.
Is simple interest useful for HSC Mathematics Standard?
Yes. Financial mathematics is part of Mathematics Standard, and senior questions can involve interest, investments, loans, comparisons and financial decision-making.
Trusted NSW Mathematics Links
Curriculum note: This learning guide is designed to support NSW students from Stage 5 through Mathematics Standard 1 and Standard 2. Schools may teach content in different sequences, so students should also follow their school's assessment notification and scope-and-sequence documents.
Next step: use the interactive practice test below to move from direct formula questions to multi-step HSC-style applications.
