Use the simple interest formula to calculate interest earned or charged, find unknown values for principal, rate, or time, and compare simple interest investments.
Use the PDF for classwork, homework or revision. It includes key ideas, activities, questions, an extend task and success-criteria proof.
If you put $5,000 in a bank account that pays 4% interest per year, how much would you have after 3 years? Most people guess $5,600 — but is that right? Simple interest assumes the bank pays you the same dollar amount every single year, based only on your original deposit. It never grows on itself. Compare this to putting that same $5,000 under your mattress — at least the bank is paying you something. But is simple interest actually a good deal for a borrower, or a lender? Think about who benefits from interest being "simple" rather than compounding.
Apply $I = Prn$ to calculate simple interest, and $A = P + I$ for the total amount
Rearrange $I = Prn$ to find the unknown principal, rate, or number of periods
Convert between different time periods ensuring $r$ and $n$ use the same unit
Compare simple interest investments and solve "time to reach target amount" problems
Wrong: Simple interest earns interest on the interest already accumulated.
Right: Simple interest is calculated only on the principal: I = P × r × n. Only compound interest earns interest on previously accumulated interest.
Simple interest is calculated only on the original principal — it does not grow on previously earned interest, making it predictable and linear over time.
In the formula $I = Prn$: $P$ is the principal (the original amount invested or borrowed), $r$ is the interest rate expressed as a decimal per time period (so 6% per annum = 0.06), and $n$ is the number of time periods. The time period for $r$ and $n$ must match — if $r$ is a per annum rate, $n$ must be in years; if $r$ is a monthly rate, $n$ must be in months. The formula gives $I$, the total interest earned or charged. To find the total amount, use $A = P + I$. Simple interest grows linearly — the same dollar amount is added each period.
HSC questions don't always ask you to find $I$ — they may give you the interest and ask for the principal, rate, or time instead, requiring you to rearrange the formula.
The formula $I = Prn$ can be rearranged to find any one variable if the other three are known:
A reliable method is to substitute the known values into $I = Prn$ first, then solve for the unknown algebraically. Always check your answer by substituting all values back into $I = Prn$ to verify.
When choosing between two simple interest options, convert both to the same basis — either total interest earned or effective annual rate — before comparing.
HSC comparison questions often describe two investment or loan options with different principals, rates, and terms and ask which is better. Strategy: calculate $I$ for each option using $I = Prn$, then compare. If the principals differ, comparing raw interest amounts may be misleading — instead calculate the effective annual interest rate ($I \div P \div \text{years} \times 100$) for a fair comparison.
Another common format gives a target amount (e.g. "how long until the investment reaches $8,000?") — set $A = P + I = P + Prn$ and solve for $n$. Find the required interest first: $I = A - P$, then $n = I \div (Pr)$.
Simple interest questions often feel different on the surface, but most of them reduce to the same small set of setups once you identify what is being asked for.
| If the question asks for... | Best starting step |
|---|---|
| Total amount after a given time | Find $I = Prn$, then add $A = P + I$ |
| Unknown rate | Find or identify $I$, then use $r = \frac{I}{Pn}$ |
| Unknown time | Find the required interest first, then use $n = \frac{I}{Pr}$ |
| Comparison of two options | Calculate interest or total amount for both on the same time basis |
| Months with annual rate | Convert months to years or annual rate to a monthly rate |
Yuki invests $12,500 at a simple interest rate of 5.2% per annum for 3 years. Calculate: (a) the interest earned, and (b) the total amount at the end of 3 years.
Identify variables: $P = \$12{,}500$, $r = 0.052$, $n = 3$
Convert 5.2% per annum to a decimal: 5.2 ÷ 100 = 0.052. Rate and time are both annual, so the periods match.
Lena borrows $8,400 and repays $9,576 after 2 years under a simple interest arrangement. What was the annual interest rate?
$$I = A - P = \$9{,}576 - \$8{,}400 = \$1{,}176.00$$
The interest is the difference between what Lena repaid and what she borrowed.
How many months will it take for an investment of $6,000 at 4.8% per annum simple interest to grow to $6,840?
$$I \text{ needed} = \$6{,}840 - \$6{,}000 = \$840$$
Find the required interest — the difference between target amount and principal.
Option A invests $8,000 at 4.6% per annum simple interest for 5 years. Option B invests $8,000 at 4.2% per annum simple interest for 6 years.
Which option gives the greater total amount, and by how much?
$$I_A = \$8{,}000 \times 0.046 \times 5 = \$1{,}840$$
$$A_A = \$8{,}000 + \$1{,}840 = \$9{,}840$$
Calculate the simple interest first, then add it to the principal to find the total amount for Option A.
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
5 random questions from a replayable lesson bank — feedback shown immediately
Simple interest of $1,755 is earned on a principal of $13,500 over 3 years. What is the annual interest rate?
An investment of $5,500 earns simple interest at 6% per annum. How many years until the total amount reaches $7,150?
A loan of $4,800 earns simple interest of $432 over 18 months. What annual simple interest rate was charged?
These questions practise setting up the variables carefully and making the time units match before substituting.
Find the simple interest earned on $7,200 invested at 4.5% per annum for 18 months.
An account earns $1,020 simple interest in 4 years at 3.4% per annum. Find the principal.
Compare two investments: Option A is $9,500 at 4.1% simple interest for 3 years; Option B is $9,500 at 3.8% simple interest for 4 years. Which gives the greater total amount?
Climb platforms using your knowledge of simple interest calculations. Pool: lessons 1–11.
Use this as a quick recognition drill: decide what the unknown is, then choose the correct setup before calculating.
If a question asks for the total amount after simple interest, what should happen after finding $I$?
An annual rate is given but the time is in months. What is the key thing to do before substituting?
Which rearrangement correctly finds the simple interest rate?
What makes a comparison answer complete when two simple interest options are compared?