Compound Interest & Depreciation –

Compound interest and depreciation are percentage-based calculations that crop up regularly in GCSE Maths exams across AQA, Edexcel and OCR. Unlike simple interest, compound interest is calculated on a growing (or shrinking) amount each year, which makes the mathematics more interesting and more reflective of real life. Whether you are working out how much an investment is worth after several years or how quickly a car loses value, the same multiplier method applies. This guide takes you through the key formulas, provides fully worked examples at Foundation and Higher level, flags the common errors examiners report, and gives you practice questions to sharpen your skills. For a broader look at essential formulas, see our GCSE Maths formulas guide.

What Is Compound Interest?

Compound interest means you earn (or pay) interest on the original amount and on any interest already accumulated. Each year, the amount grows by a percentage of the new total rather than the original amount.

The Multiplier Method

The most efficient way to handle compound interest at GCSE is the multiplier method. To increase an amount by r%, multiply by:

$$\text{Multiplier} = 1 + \frac{r}{100}$$

For example, a 5% increase uses a multiplier of 1.05.

The Compound Interest Formula

For n years of compound interest at rate r% on a starting amount P:

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

Where A is the final amount after n years.

What Is Depreciation?

Depreciation is the opposite — the value decreases by a fixed percentage each year. The multiplier for a decrease of r% is:

$$\text{Multiplier} = 1 - \frac{r}{100}$$

So a 15% depreciation uses a multiplier of 0.85. The formula becomes:

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

Simple Interest vs Compound Interest

With simple interest, you calculate the same fixed amount of interest every year based on the original principal. With compound interest, each year's interest is calculated on the running total. Over time, compound interest produces a larger amount because the base keeps growing.

Step-by-Step Method

Compound Interest

1. Identify the starting amount (P), the percentage rate (r), and the number of years (n).
2. Work out the multiplier: 1 + r/100.
3. Raise the multiplier to the power n.
4. Multiply the starting amount by the result.
5. If the question asks for just the interest earned, subtract the original amount from the final amount.

Depreciation

1. Identify P, r, and n as before.
2. Work out the multiplier: 1 − r/100.
3. Raise the multiplier to the power n.
4. Multiply the starting amount by the result.
5. If the question asks how much value has been lost, subtract the final amount from the original.

Finding the Number of Years (Higher)

Sometimes a Higher-tier question asks how many years it takes for an amount to exceed or fall below a given value. Use trial and improvement — calculate the value year by year until you pass the target.

Worked Example 1 — Foundation Level

Sarah invests £2,000 in a savings account that pays 3% compound interest per year. How much is in the account after 4 years?

Step 1: Identify the values: P = £2,000, r = 3%, n = 4.

Step 2: Work out the multiplier: 1 + 3/100 = 1.03.

Step 3: Raise to the power 4: 1.03⁴ = 1.12550881.

Step 4: Multiply: £2,000 × 1.12550881 = £2,251.02 (to the nearest penny).

Answer: After 4 years, the account contains £2,251.02.

If the question asked for the interest earned, you would subtract the original: £2,251.02 − £2,000 = £251.02.

Worked Example 2 — Higher Level

A car is bought for £18,500. It depreciates by 12% in the first year and 9% each year after that. What is the car worth after 5 years? Give your answer to the nearest pound.

Step 1: Year 1 uses a multiplier of 1 − 12/100 = 0.88. Years 2–5 use a multiplier of 1 − 9/100 = 0.91.

Step 2: After year 1: £18,500 × 0.88 = £16,280.

Step 3: Years 2 to 5 is 4 more years at 9%: multiplier = 0.91⁴ = 0.68574961.

Step 4: £16,280 × 0.68574961 = £11,163.61.

Answer: The car is worth approximately £11,164 after 5 years.

Notice how the question uses two different rates — read carefully to spot this in exams.

Common Mistakes

• Using simple interest instead of compound interest. If the question says "compound", you must use the multiplier raised to the power n, not multiply the interest by n.
• Wrong multiplier direction. Increase → multiply by (1 + r/100). Decrease → multiply by (1 − r/100). Mixing these up is a very common error.
• Forgetting to answer the actual question. Some questions ask for the interest or the loss, not the final amount. Always re-read what is being asked.
• Rounding too early. Keep the full decimal in your calculator until the very end, then round. Rounding intermediate values can lead to an inaccurate final answer.
• Confusing the number of years. If someone invests at the start of 2020 and withdraws at the end of 2024, that is 5 years of interest, not 4.

Exam Tips

• Write the multiplier clearly in your working. Examiners award method marks for showing the correct multiplier.
• Use your calculator efficiently. Type P × multiplier^n in one go rather than multiplying year by year — it is faster and reduces errors.
• For "how many years" questions on Higher, set up a table showing the value at the end of each year. The answer is the year where the value first passes the target.
• Check your answer makes sense. If a value is depreciating, the final answer must be smaller than the start. If interest is being added, it must be larger.
• Show clear units — always include the £ sign and give monetary answers to two decimal places (or as instructed).

Practice Questions

Question 1 (Foundation) James invests £5,000 at 4% compound interest per year. How much does he have after 3 years?

Question 2 (Foundation) A laptop costing £800 depreciates by 20% each year. What is it worth after 2 years?

Question 3 (Higher) £6,000 is invested at 2.5% compound interest. After how many complete years will the investment first exceed £7,000?

Question 4 (Higher) A painting is bought for £3,200 and appreciates by 6% per year. A vase is bought for £4,500 and depreciates by 10% per year. After how many complete years is the painting worth more than the vase?

Ready to practise compound interest and depreciation with questions tailored to your level? Create your free GCSEMathsAI account and start generating personalised questions today.

Related Topics

• Percentages — understanding percentage increase and decrease underpins this topic
• Growth and Decay — extends compound change to exponential models (Higher)
• Ratio and Proportion — connects proportional reasoning with multiplicative change
• Fractions, Decimals and Percentages — converting between forms is essential

Summary

Compound interest and depreciation both use the multiplier method. For compound interest, multiply by (1 + r/100) raised to the power n. For depreciation, multiply by (1 − r/100) raised to the power n. Always identify whether the question asks for the final amount or the change. Show your multiplier clearly, keep full decimals until the final step, and check the direction of change makes sense. These topics appear frequently on both Foundation and Higher papers and are reliable marks once the method is secure.