Simple Interest
Discover how banks calculate interest on your savings and loans using the simple interest formula - the foundation of all interest calculations.
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Worksheet
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Q1 · What do you know about how banks pay you interest on savings?
Q2 · If you invest $1,000 at 5% per year for 3 years, how much interest do you think you would earn?
Learning Intentions
Know
- The simple interest formula and each of its variables.
- The difference between simple interest and the total amount.
Understand
- Why simple interest is called “simple”: the interest is calculated only on the principal each period.
- How interest rates, time and principal affect total interest earned or paid.
Can Do
- Calculate simple interest given principal, rate and time.
- Calculate total amount (principal + interest).
- Rearrange the formula to find any missing variable.
Success Criteria
- I can use the formula $I = PRT$ to calculate simple interest.
- I can calculate the total amount using $A = P + I$ or $A = P(1 + RT)$.
- I can find the principal, rate or time when given the other variables.
- I can interpret simple interest in real-world contexts (term deposits, personal loans, hire purchase).
Key Terms
Common Mistakes to Avoid
Wrong: “Simple interest gets bigger each year because it compounds.” Simple interest is constant each year because it is always calculated on the original principal only.
Right: Simple interest per year = $P \times R$ (as a decimal). It never changes. Total interest = $P \times R \times T$.
Wrong: Forgetting to convert the rate from a percentage to a decimal before multiplying. $5\%$ must become $0.05$.
Right: Always divide the percentage rate by 100 before substituting into $I = PRT$. Or use $I = \dfrac{PRT}{100}$ if $R$ is left as a percentage.
When you put money in a savings account or take out a personal loan, the bank calculates how much extra you earn or owe. Simple interest is the most straightforward way to do this.
Simple interest assumes the interest is calculated on the original principal only, every year. It does not earn interest on interest.
Converting time to years is essential:
- 6 months = $0.5$ years
- 3 months = $0.25$ years
- 18 months = $1.5$ years
- 90 days = $\dfrac{90}{365}$ years (use 365 unless told otherwise)
Real-World Anchor: Australian term deposits from banks like Commonwealth, NAB and ANZ often use simple interest for short-term deposits under 12 months. A $10,000 term deposit at 4.5% p.a. for 6 months earns $10,000 \times 0.045 \times 0.5 = $225 in interest.
What to write in your book
- Simple interest is calculated only on the original principal: $I = P \times R \times T$.
- Always convert the rate to a decimal and the time to years before substituting.
- The total amount can be found using $A = P + I$ or $A = P(1 + RT)$.
- Time conversions: 6 months = 0.5 years, 3 months = 0.25 years, 90 days = $\frac{90}{365}$ years.
Interactive: Simple Interest Calculator
Your Turn
Question 1: Calculate the simple interest on $8,000 invested at 5.5% p.a. for 4 years.
Question 2: A loan of $3,500 attracts simple interest at 8% p.a. How much interest is paid after 9 months?
Question 3: An investment earns $450 in simple interest over 2.5 years at 3% p.a. What was the principal?
Revisit Your Thinking
Look back at your Think First answer about $1,000 at 5% for 3 years. Calculate the exact interest and total amount using the formula. Did your estimate match? What surprised you about how simple interest works?
Earlier you were asked: What was your first thought on this topic?
Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?
What is the simple interest on $4,000 invested at 6% p.a. for 3 years?
A loan of $6,000 attracts simple interest at 5.5% p.a. How much interest is paid after 6 months?
An investment earns $560 in simple interest over 4 years at 4% p.a. What was the principal?
Which formula correctly gives the total amount $A$ for simple interest?
$15,000 is invested at 4.8% p.a. simple interest for 90 days. Calculate the interest earned.
Maya invests $7,500 in a term deposit paying 4.2% p.a. simple interest for 18 months. Calculate the total amount she will receive at maturity.
A small business takes out a short-term loan. They borrow $20,000 and after 8 months repay a total of $20,800.
(a) Calculate the interest paid. (1 mark)
(b) Calculate the annual simple interest rate, as a percentage. (2 marks)
(c) If the loan was for 2 years at the same rate, how much total interest would be paid? (1 mark)
Two banks offer different term deposit rates. Bank A offers 3.8% p.a. simple interest for 2 years. Bank B offers 4.2% p.a. simple interest for 18 months. Zara has $12,000 to invest.
(a) Calculate the total amount from Bank A. (2 marks)
(b) Calculate the total amount from Bank B. (2 marks)
(c) Which bank gives the better return? Justify your answer with calculations. (1 mark)
Simple interest
$I = PRT$ — calculated on the principal only
Total amount
$A = P + I = P(1 + RT)$
Principal ($P$)
The initial amount of money invested or borrowed
Rate ($R$)
Annual interest rate expressed as a decimal
Time ($T$)
Duration in years (convert months and days)
Rearranging
$P = \frac{I}{RT}$, $R = \frac{I}{PT}$, $T = \frac{I}{PR}$
Real-Life Link
In Australia, the Australian Securities and Investments Commission (ASIC) regulates how banks display interest rates. When you see a term deposit advertised at “4.5% p.a.”, that is the simple annual rate for the full year. Short-term deposits under 12 months almost always use simple interest. Understanding this formula lets you compare bank offers accurately and know exactly how much your money will grow.
Game Time!
Test your simple interest skills in an interactive challenge.
Play Simple Interest Challenge