Compound Interest and Depreciation
Compound interest and depreciation describe how an amount of money or an item's value grows or shrinks by the same percentage each year, with each year's change worked out on the new total rather than the original amount. It appears in GCSE Ratio, Proportion and Rates of Change questions about savings, loans and car or equipment values, and is usually solved with a single multiplier raised to a power.
Before you start
Make sure you're comfortable with these topics first:
Method
- Work out the multiplier for one year's change: add the percentage as a decimal to 1 for an increase (e.g. a 4% increase is 1.04), or subtract it from 1 for a decrease (e.g. a 15% decrease is 0.85).
- Raise the multiplier to the power of the number of years, since each year's growth or decay compounds on the previous year's total, not the original amount.
- Multiply the starting amount by this power to find the final value.
- To find the interest earned or the amount lost in value, subtract the starting amount from the final value.
- If the rate changes partway through, apply each multiplier for the number of years it lasts, then multiply all the multipliers together.
- Round money answers to the nearest penny (2 decimal places) unless the question tells you otherwise.
Worked example
Ravi invests 1500 pounds in an account that pays compound interest at a rate of 3% per year. Work out the value of his investment after 4 years. Give your answer to the nearest penny.
- The multiplier for a 3% increase is 1 + 0.03 = 1.03.
- Value after 4 years = 1500 x 1.03^4.
- 1.03^2 = 1.0609, so 1.03^4 = 1.0609 x 1.0609 = 1.12550881.
- 1500 x 1.12550881 = 1688.263215.
- Round to the nearest penny: 1688.26.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
A laptop is bought for 900 pounds. It depreciates in value by 20% per year. Work out its value after 3 years.
Zara invests 1800 pounds in a savings account that pays compound interest at a rate of 2% per year. Calculate the total interest she earns after 3 years. Give your answer to the nearest penny.
Tariq invests 1200 pounds for 4 years. He compares two accounts. Account A pays simple interest at 3.5% per year. Account B pays compound interest at 3% per year. (a) Calculate the total in Account A after 4 years. (2) (b) Calculate the total in Account B after 4 years, to the nearest penny. (3)
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