Sheet № 38 · Foundation + Higher · AQA · Edexcel · OCR
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 wo
§Key definitions
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.
§Formulas to memorise
\text{Multiplier} = 1 + \frac{r}{100}
A = P \times \left(1 + \frac{r}{100}\right)^n
\text{Multiplier} = 1 - \frac{r}{100}
A = P \times \left(1 - \frac{r}{100}\right)^n
Worked example
See example below.
Sarah invests £2,000 in a savings account that pays 3% compound interest per year. How much is in the account after 4 years?
⚠ 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).