Simple interest
Simple interest uses the original principal at a fixed rate. The principal is the amount invested or borrowed. Interest is the extra money earned or owed. For the model used here, the principal and rate stay fixed and there are no fees
\[\begin{aligned}I&=P\times\frac{r}{100}\times t\\A&=P+I\end{aligned}\]
- Use the right quantities P is the principal, I is the interest and A is the final amount, all in dollars. The letter r is the annual percentage number and t is time in years. The abbreviation p.a. means per year
- Convert months Divide months by twelve. Leave a non-terminating conversion as an exact fraction \(\displaystyle t=\frac{\text{months}}{12}\)
- Find interest or the final amount Multiply the original principal by the rate factor and the term in years. Add the principal only when the final amount is requested
- Find a missing quantity Substitute what is known and divide by the factors multiplying the unknown. The rate formula gives a percentage number \(\displaystyle \begin{aligned}t&=\frac{100I}{Pr}\\P&=\frac{100I}{rt}\\r&=\frac{100I}{Pt}\end{aligned}\)
- Check the model A withdrawal, a repayment that changes the principal, a rate change or a fee needs to be accounted for. A single fixed-principal calculation may no longer fit
Common mistakes
Using months as years
✕\(\displaystyle \begin{aligned}I&=1{,}950\times0.064\times10\\I&=1{,}248\end{aligned}\)✓\(\displaystyle \begin{aligned}t&=\frac{10}{12}\\I&=1{,}950\times0.064\times t\\I&=104\end{aligned}\)
An annual rate needs the term in years. Keep the fraction exact until the endGiving interest as the final amount
✕\(\displaystyle A=104\)✓\(\displaystyle \begin{aligned}A&=1{,}950+104\\A&=2{,}054\end{aligned}\)
The interest is only the extra amount. The final amount also includes the principalConfusing the percentage number and decimal rate
✕\(\displaystyle r=0.072\)✓\(\displaystyle r=7.2\)
In this rule, the rate variable is the percentage number. The decimal rate is the multiplier after division by one hundredDifficulty levels
introFind interest or the final amount for whole-year terms
standardFind interest or the final amount when the term is in months
challengeFind a missing principal, rate or time, or compare different rates and terms
examChoose interest or a final amount from plausible numerical answers
Questions about this topic
Why convert months to years?+
An annual rate describes one year. The time in the rule must use the same unit
Why is the interest equal in equal periods?+
The principal and rate stay fixed, so each equal period adds the same amount
What if the question gives the final amount?+
Subtract the principal to find the interest before finding a missing rate or time
Does the option with the higher rate always earn more?+
The term matters too. Compare total interest over the stated terms and say which comparison you made
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 1: Number and financial mathematics
In this chapter
Evaluate an integer expressionFactors, multiples, HCF, LCM and primesRound to decimal places or significant figuresEstimate an expression using rounded inputsConvert between fractions, mixed numbers and decimalsClassify real numbers and compare exact valuesAdd, subtract, multiply and divide fractions and mixed numbersWrite a ratio from countsWrite ratios in simplest formComplete equivalent ratiosUse a constant rateDivide a quantity in a given ratioDecide which option is the better valueConvert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1F Percentages and money: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changePercentage error against a reference value1G Percentage change and percentage error: Find the original amount from a percentageProfit, mark-up and discountIncome and taxSimple interestCompound interest (optional extension)