Compound Interest Calculations – GCSE Maths Revision Guide

Compound interest is tested on both Foundation and Higher GCSE papers. Unlike simple interest, where the same amount is added each year, compound interest grows on the accumulated total — meaning your money (or debt) increases faster over time. This guide covers the multiplier method, the compound interest formula, depreciation, and the key difference between simple and compound interest.

What Is Compound Interest?

Compound interest is interest calculated on the original amount and on any interest already earned. Each year, the interest is added to the running total, so the next year's interest is calculated on a larger amount.

For example, £1,000 at 5% compound interest earns £50 in year one (total £1,050), then £52.50 in year two (5% of £1,050, total £1,102.50), and so on. The amount grows faster each year because the base keeps increasing.

Simple interest, by contrast, is calculated on the original amount only. The same £1,000 at 5% simple interest earns £50 every year regardless of what has accumulated. Over time, compound interest always produces a larger total than simple interest at the same rate.

Key Formulas

A = P × (1 + r/100)^n — compound interest (growth)

A = P × (1 − r/100)^n — depreciation (decay)

Multiplier for r% increase = 1 + r/100

Multiplier for r% decrease = 1 − r/100

Step-by-Step Method

Identify the starting amount P, the percentage rate r, and the number of years n.
Calculate the multiplier: for growth use 1 + r/100; for depreciation use 1 − r/100.
Raise the multiplier to the power n.
Multiply the starting amount by the result.
Answer the question — check whether it asks for the final amount or the interest/loss only.

Worked Example 1 — Foundation Level

Question: Emily invests £3,000 at 4% compound interest per year. How much is in the account after 3 years?

Working: Multiplier = 1 + 4/100 = 1.04. A = £3,000 × 1.04³ = £3,000 × 1.124864 = £3,374.59 (to the nearest penny).

Answer: After 3 years, the account contains £3,374.59.

Worked Example 2 — Higher Level

Question: A car worth £16,000 depreciates by 15% in the first year and 10% per year after that. Find its value after 4 years to the nearest pound.

Working: After year 1: £16,000 × 0.85 = £13,600. Years 2–4 (3 years at 10%): multiplier = 0.90³ = 0.729. Value after 4 years: £13,600 × 0.729 = £9,914.40.

Answer: The car is worth approximately £9,914 after 4 years.

Worked Example 3 — Exam Style

Question: Marcus invests £4,500 at 3% compound interest. After how many complete years will the investment first exceed £5,000?

Working: A = £4,500 × 1.03^n. Test each year: Year 1: £4,500 × 1.03 = £4,635.00 Year 2: £4,635.00 × 1.03 = £4,774.05 Year 3: £4,774.05 × 1.03 = £4,917.27 Year 4: £4,917.27 × 1.03 = £5,064.79

Answer: After 4 complete years, the investment first exceeds £5,000.

Common Mistakes

Using simple interest when compound is required. If the question says "compound", you must use the multiplier raised to the power n, not multiply the yearly interest by n.
Wrong multiplier direction. An increase of 8% uses multiplier 1.08. A decrease of 8% uses multiplier 0.92. Mixing these up loses all marks.
Rounding too early. Keep full decimal precision in your calculator until the final step, then round as instructed.

Exam Tips

Write the multiplier clearly — examiners specifically look for it and award a method mark.
Use the power button on your calculator: type P × multiplier^n in one go for speed and accuracy.
If the question asks for the interest earned, subtract the original amount from the final amount.

Practice Questions

Q1 (Foundation): £2,500 is invested at 6% compound interest. Find the value after 2 years.

Answer: Multiplier = 1.06. A = £2,500 × 1.06² = £2,500 × 1.1236 = £2,809.00.

Q2 (Foundation): A phone worth £700 depreciates by 25% each year. What is it worth after 3 years?

Answer: Multiplier = 0.75. A = £700 × 0.75³ = £700 × 0.421875 = £295.31.

Q3 (Higher): Compare the final values: £10,000 at 5% simple interest for 6 years versus £10,000 at 5% compound interest for 6 years.

Answer: Simple: Interest = £10,000 × 0.05 × 6 = £3,000, so total = £13,000. Compound: A = £10,000 × 1.05⁶ = £10,000 × 1.340096 = £13,400.96. Compound interest gives £400.96 more.

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Summary

Compound interest is calculated on the running total, not just the original amount.
Use the multiplier method: multiply by (1 + r/100)^n for growth, or (1 − r/100)^n for depreciation.
Simple interest gives the same amount each year; compound interest grows faster over time.
Always identify whether the question asks for the final amount or the interest/loss only.
Show your multiplier clearly and do not round until the final step.

Compound Interest Calculations –