Simple Interest
Simple interest is calculated only on the original principal — the same dollar amount is added every period. Master $I = Prn$, learn to rearrange for any unknown, convert time units, and compare investments. The formula $I = Prn$ is the engine of this entire lesson.
Practise this lesson
Three printable worksheets that build from foundations to mastery — or build your own from any module’s questions.
If you put $5,000 in a bank account that pays 4% interest per year, how much would you have after 3 years? 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. Who do you think benefits more from simple interest — the borrower or the lender?
Without calculating — write your gut feeling. We'll revisit this at the end of the lesson.
Simple interest in Maths Standard centres on three formulas. Lock these in before the worked examples.
$I = Prn$ gives the interest earned or charged. $A = P + I$ gives the total amount. The rearrangements let you solve for any unknown when the other three values are known.
Key facts
- The simple interest formula $I = Prn$
- The total amount formula $A = P + I$
- The rearrangements for $P$, $r$, and $n$
- That simple interest grows linearly
- That $r$ and $n$ must use matching time units
Concepts
- Why simple interest is only calculated on the original principal
- Why mismatched time units give wrong answers
- How to compare two investments on the same basis
- The difference between simple and compound interest (preview)
Skills
- Calculate $I$ and $A$ for any principal, rate, and time
- Rearrange to find unknown $P$, $r$, or $n$
- Convert months to years and vice versa for $n$
- Compare two investment options and state the better one with the dollar difference
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 formula gives $I$, the total interest earned or charged. To find the total amount, use $A = P + I$.
What to write in your book
- $I = Prn$ — convert rate to decimal first; match time units for $r$ and $n$.
- $A = P + I$ — always add interest to principal for the total amount.
- Rearrangements: $P = I \div (rn)$; $r = I \div (Pn)$; $n = I \div (Pr)$.
- After finding $r$, multiply by 100 and state the unit (% per annum, etc.).
Quick check: An investment earns simple interest at 5% per annum. What value of $r$ should be substituted into $I = Prn$?
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:
- Finding $P$: $P = I \div (rn)$
- Finding $r$: $r = I \div (Pn)$ — then multiply by 100 to express as a percentage
- Finding $n$: $n = I \div (Pr)$ — the answer is in the same time unit as $r$
What to write in your book
- To find $r$: rearrange to $r = I \div (Pn)$, solve, then multiply by 100 for percentage.
- To find $n$: rearrange to $n = I \div (Pr)$. Units of $n$ match units of $r$.
- For "how long to reach $X$": find the required interest first $I = A - P$, then use $n = I \div (Pr)$.
True or false: To find the interest rate from $I = Prn$, rearrange to get $r = I \div (Pn)$, then multiply the result by 100 to convert to a percentage.
Worked examples · 4 problems, reveal step by step
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.
$P = \$12{,}500$, $r = 0.052$, $n = 3$
$I = Prn = \$12{,}500 \times 0.052 \times 3 = \$1{,}950.00$
$A = P + I = \$12{,}500 + \$1{,}950 = \$14{,}450.00$
Lena borrows $8,400 and repays $9,576 after 2 years under a simple interest arrangement. What was the annual interest rate?
$I = A - P = \$9{,}576 - \$8{,}400 = \$1{,}176.00$
$r = \dfrac{I}{Pn} = \dfrac{\$1{,}176}{\$8{,}400 \times 2} = 0.07$
Rate $= 0.07 \times 100 = 7\%$ per annum
How many months will it take for an investment of $6,000 at 4.8% per annum simple interest to grow to $6,840?
$I = \$6{,}840 - \$6{,}000 = \$840$
$r = 0.048 \div 12 = 0.004$ per month
$n = \dfrac{I}{Pr} = \dfrac{\$840}{\$6{,}000 \times 0.004} = 35$ months
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?
$I_A = \$8{,}000 \times 0.046 \times 5 = \$1{,}840$
$A_A = \$8{,}000 + \$1{,}840 = \$9{,}840$
$I_B = \$8{,}000 \times 0.042 \times 6 = \$2{,}016$
$A_B = \$8{,}000 + \$2{,}016 = \$10{,}016$
Difference $= \$10{,}016 - \$9{,}840 = \$176$
$\therefore$ Option B gives the greater total amount by $\$176$.
What to write in your book
- For "time to reach target" questions: find $I = A - P$ first, then $n = I \div (Pr)$.
- Comparison answers must name the better option AND give the dollar difference.
- Don't confuse $A = P(1+rn)$ (simple, linear) with $A = P(1+r)^n$ (compound, exponential).
Fill the gap: An investment of $7,200 earns simple interest at 4.5% per annum for 18 months. The interest earned is $ (18 months = 1.5 years; $I = 7200 \times 0.045 \times 1.5$).
Common errors · the 3 traps that cost marks
What to write in your book
- Rate always as decimal before substituting: 6% → 0.06.
- 18 months at annual rate: convert to 1.5 years or convert rate to monthly (÷ 12).
- "Interest" means $I$; "total amount" means $A = P + I$. Read the question carefully.
Match each setup:
Quick-fire practice · 5 calculations
Calculate the simple interest on $5,000 at 3.6% per annum for 4 years.
Find the total amount for $9,000 at 5% per annum simple interest for 3 years.
An account earns $1,020 simple interest in 4 years at 3.4% per annum. Find the principal.
A loan of $4,800 earns simple interest of $432 over 18 months. What annual simple interest rate was charged?
An investment of $5,500 earns simple interest at 6% per annum. How many years until the total amount reaches $7,150?
Top 3 list: Name THREE things you must check before substituting values into $I = Prn$.
Look back at what you wrote in the Think First section. $5,000 at 4% for 3 years: $I = 5000 \times 0.04 \times 3 = \$600$, so $A = \$5,600$ — the guess was right. Simple interest benefits borrowers (they never pay interest on accumulated interest) but is less favourable for investors than compound interest over long periods.
What has changed? What did you get right? What surprised you?
Pick your answer, then rate your confidence — that tells the system what to drill next. Each retry pulls a fresh mix from the bank.
SA 1. Find the simple interest earned on $7,200 invested at 4.5% per annum for 18 months. (2 marks)
SA 2. An account earns $1,020 simple interest in 4 years at 3.4% per annum. Find the principal. (2 marks)
SA 3. 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, and by how much? (3 marks)
📖 Comprehensive answers (click to reveal)
Drill 1: $I = 5000 \times 0.036 \times 4 = \$720$ · 2: $A = 9000 + 9000 \times 0.05 \times 3 = \$10{,}350$ · 3: $P = 1020 \div (0.034 \times 4) = \$7{,}500$ · 4: 18 months = 1.5 years; $r = 432 \div (4800 \times 1.5) = 0.06 = 6\%$ p.a. · 5: $I = 7150 - 5500 = 1650$; $n = 1650 \div (5500 \times 0.06) = 5$ years
SA 1 (2 marks): Convert: 18 months = 1.5 years [1]. $I = 7200 \times 0.045 \times 1.5 = \$486.00$ [1].
SA 2 (2 marks): $P = I \div (rn)$ [1]. $P = 1020 \div (0.034 \times 4) = 1020 \div 0.136 = \$7{,}500.00$ [1].
SA 3 (3 marks): Option A: $I = 9500 \times 0.041 \times 3 = \$1{,}168.50$; $A = \$10{,}668.50$ [1]. Option B: $I = 9500 \times 0.038 \times 4 = \$1{,}444.00$; $A = \$10{,}944.00$ [1]. Option B is greater by $\$10{,}944.00 - \$10{,}668.50 = \$275.50$ [1].
Five timed questions on simple interest. Beat the boss to bank a tier — gold (90% + speed), silver (75%), or bronze (50%). Replays welcome.
⚔ Enter the arenaClimb platforms by answering questions on simple interest. Pool: lessons 1–11.
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