Number
Grade 5-7Compound Interest & Depreciation
Compound interest and depreciation both apply the same percentage change repeatedly, year after year, rather than just once, and the trap is treating it like simple interest by multiplying the percentage by the number of years instead. This lesson covers the multiplier method for compound interest and depreciation, the formula A = P(1 ± r/100)ⁿ, and questions where the rate changes between years.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Compound interest with the multiplier method
Convert the interest rate to a decimal multiplier by adding it to 100%, then raise that multiplier to the power of the number of years, and multiply by the original amount.
£2000 invested for 3 years at 5% compound interest: the multiplier is 1.05, so the value after 3 years is 2000 × 1.05³ = £2315.25.
Depreciation with the multiplier method
Depreciation works the same way as compound interest, except the decimal multiplier is found by subtracting the percentage from 100%, since the value falls each year rather than growing.
A car bought for £12,000 that depreciates by 15% per year: the multiplier is 0.85, so its value after 2 years is 12,000 × 0.85² = £8670.
The compound interest and depreciation formula
The formula A = P(1 + r/100)ⁿ gives the value after growth, where P is the original amount, r is the percentage rate, and n is the number of years. For depreciation, use A = P(1 - r/100)ⁿ instead.
£6000 invested for 4 years at 2.5% compound interest: A = 6000 × (1 + 2.5/100)⁴ = 6000 × 1.025⁴ = £6622.88.
Finding the total interest or amount depreciated
When a question asks for the interest earned or the amount lost in value, rather than the final amount, work out the final amount first, then subtract the original amount.
£4000 invested for 2 years at 3% compound interest gives 4000 × 1.03² = £4243.60. The interest earned is £4243.60 - £4000 = £243.60.
Worked Examples
Three exam-style questions, fully solved.
£2000 is invested for 3 years at 5% compound interest per year. Work out the value of the investment after 3 years.
Easy- 1.Convert 5% to a decimal multiplier: 1.05
- 2.Raise the multiplier to the power of the number of years: 1.05³
- 3.Multiply by the original amount: 2000 × 1.05³
Answer: £2315.25
£4000 is invested for 2 years at 3% compound interest per year. Work out the total interest earned.
Medium- 1.Convert 3% to a decimal multiplier: 1.03
- 2.Work out the final amount: 4000 × 1.03² = £4243.60
- 3.Subtract the original amount to find the interest earned: £4243.60 - £4000
Answer: £243.60
A computer is bought for £900. It depreciates by 30% in the first year and 20% in each following year. Work out its value after 3 years, to the nearest penny.
Hard- 1.Since the rate changes, find each year's multiplier separately: year 1 is 0.7, years 2 and 3 are each 0.8
- 2.Multiply the original amount by each year's multiplier in turn: 900 × 0.7 × 0.8 × 0.8
Answer: £403.20
Avoid These
The most common mistakes students make.
Using simple interest instead of compound interest, by multiplying the percentage by the number of years and adding it all in one step, instead of applying the multiplier repeatedly.
Giving the final amount when the question asks for the interest earned or the amount lost in value, instead of subtracting the original amount from the final amount.
Using a decimal multiplier above 1 for depreciation, or below 1 for growth, which applies the change in the wrong direction.
Rounding the decimal multiplier or an intermediate value too early, which makes the final answer inaccurate.
Using the same multiplier for every year when the rate changes between years, instead of multiplying by each year's own rate in turn.
FAQ
Questions parents and students ask.
Before this topic, make sure you know
What to learn next
Want a plan built around your child specifically?
Get our free 8-video course, or book a free Roadmap Call for a personalised plan.