Common mistakes with compound interest in GCSE maths

Compound interest: fix the method, not just the answer

The most common mistakes with compound interest in GCSE maths are using simple interest, choosing the wrong multiplier and answering a different question from the one asked. The reliable method is to multiply the starting amount by the percentage multiplier for each interest period, keep your calculator's accuracy, then check whether you need the final balance or the interest earned.

Imagine a student checking a marked question. Their arithmetic looks sensible, but their answer is wrong. Rather than doing another question immediately, they trace the first decision that went wrong. That is where useful revision begins.

Let's follow that process through the compound interest mistakes that can turn a familiar question into an avoidable error.

Your compound interest checklist

Before calculating, identify:

• The starting amount.
• The percentage rate and whether it changes.
• How often interest is added.
• The number of interest periods.
• Whether the question asks for the balance, interest or original amount.

For a constant rate, use:

$$A=P{\left(1+\frac{r}{100}\right)}^n$$

Here, $P$ is the principal, or starting amount; $r$ is the percentage rate per period; $n$ is the number of periods; and $A$ is the final amount. The rate and period must match. An annual rate applied annually needs a power representing years.

Mistake: calculating simple interest instead

Why it happens

Consider a hypothetical question: a student invests £1000\pounds 1000£1000 at $5\%$ compound interest per year for three years.

They calculate:

$$1000\times 0.05\times 3=150$$

Then they add this to the deposit and give £1150\pounds 1150£1150.

This is simple interest. It assumes each year's interest is calculated from the original deposit. Compound interest uses the updated balance, including interest already added.

The correct method

First, find the multiplier:

$$1+\frac{5}{100}=1.05$$

Then apply it once for each year:

$$1000\times 1.05=1050$$ $$1050\times 1.05=1102.50$$ $$1102.50\times 1.05=1157.625$$

The final balance, rounded to the nearest penny, is £1157.63\pounds 1157.63£1157.63. The interest grows because the amount earning interest grows.

The compound interest revision guide provides a useful reference when you need to revisit percentage multipliers.

Mistake: using the percentage as the multiplier

Why it happens

The student remembers that $5\%=0.05$, then calculates:

$$1000\times 0.05^3$$

The conversion is correct, but its role is wrong. Multiplying by $0.05$ finds just the interest for one period, not the balance after adding it.

The correct method

An increase of $5\%$ leaves you with $105\%$ of the previous balance. That gives a multiplier of $1.05$:

$$1000\times 1.05^3=1157.625$$

A useful check is that a positive interest rate should increase a positive balance. If your multiplier makes the savings shrink, inspect it before continuing.

Start with MathsGenie's compound interest Lessons, then use its Question Bank compound interest question to practise choosing the right multipliers yourself.

Mistake: multiplying by the number of years

Why it happens

The student understands the multiplier but writes:

$$1000\times 1.05\times 3$$

The final multiplication triples the balance. It does not apply another two years of interest.

The correct method

Three annual increases mean multiplying by $1.05$ three times:

$$1000\times 1.05\times 1.05\times 1.05=1000\times 1.05^3$$

The power counts applications of the multiplier. It is not simply a place to put every time-related number in the question.

Check the wording carefully. If the question gives an annual rate and annual compounding, use years. Do not insert a number of months into that same calculation without an appropriate rate for those periods.

A stick-figure student watches a tiny coin snowball grow, joking that they thought only the homework was accumulating.

Mistake: using one multiplier when the rate changes

Why it happens

Once the student learns the formula, it becomes tempting to use it everywhere. But a single power assumes the same multiplier applies throughout.

Suppose £1500\pounds 1500£1500 earns $2\%$ in the first year and $3\%$ in the second. Squaring either multiplier ignores one of those rates.

The correct method

Apply each rate to the balance for its own period:

$$1500\times 1.02=1530$$ $$1530\times 1.03=1575.90$$

You can combine the steps:

$$1500\times 1.02\times 1.03=1575.90$$

The final balance is £1575.90\pounds 1575.90£1575.90. Keep different multipliers separate rather than adding the rates together. MathsGenie's repeated percentage change topic develops this distinction further.

Mistake: giving the balance instead of the interest

Why it happens

The calculator produces a plausible money answer, and the student stops reading. Yet “How much is in the account?” and “How much interest has been earned?” ask for different quantities.

The correct method

Return to the original investment of £1000\pounds 1000£1000. After three years, the unrounded balance is $1157.625$.

To find the interest, subtract the deposit:

$$1157.625-1000=157.625$$

The interest earned is therefore £157.63\pounds 157.63£157.63, not £1157.63\pounds 1157.63£1157.63.

Before writing your final answer, label it mentally: balance or interest? This small pause catches an error that more calculator practice alone will not fix.

Mistake: rounding during the calculation

Why it happens

Money is normally written to two decimal places, so the student rounds every intermediate result. Those rounded values then feed into later calculations, potentially changing the final answer.

The correct method

For a standard GCSE compound interest calculation, retain full calculator accuracy until the end, unless the question specifies a different rounding method.

Enter the complete expression where possible:

$$1000\times 1.05^3$$

Then round the final answer as instructed. If the question asks for the nearest penny, use two decimal places. If it asks for the nearest pound, follow that instruction instead.

Exam-style practice: identify the trap first

For each question, write the multiplier calculation before reaching for your calculator.

• Balance: An account contains £600\pounds 600£600 and earns $4\%$ compound interest annually. Find its balance after two years.
• Interest: For the same account, find the total interest earned over those two years.
• Reverse calculation: An investment is worth £926.10\pounds 926.10£926.10 after three years at $5\%$ compound interest annually. Find the original investment.

Answers and checks

The first balance is:

$$600\times 1.04^2=648.96$$

So the interest is:

$$648.96-600=48.96$$

For the reverse calculation, divide by the complete growth multiplier:

$$P=\frac{926.10}{1.05^3}=800$$

The original investment was £800\pounds 800£800. Subtracting $15\%$ would not reverse three compound increases.

When reviewing your work, name the error rather than merely copying the answer. Was it the multiplier, the power, the rounding or the quantity requested? The compound interest exam booklet provides further questions for checking whether your correction holds up.

Turn corrections into reliable answers

Our hypothetical student does not need a completely new approach, just a method they can repeat without skipping the final check. You now have that method, but recognising an error is different from avoiding it independently. Start with MathsGenie's compound interest Lessons, then practise applying each correction in the Question Bank.