Sheet № 117 · Foundation + Higher · AQA · Edexcel · OCR
Compound Interest Calculations –
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 k
§Key definitions
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.
Question:
Emily invests £3,000 at 4% compound interest per year. How much is in the account after 3 years?
Answer:
After 3 years, the account contains £3,374.59.
Q1 (Foundation):
£2,500 is invested at 6% compound interest. Find the value after 2 years.
Q2 (Foundation):
A phone worth £700 depreciates by 25% each year. What is it worth after 3 years?
§Formulas to memorise
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
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.
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
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).
⚠ 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.