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.
What you need to know
- Compound interest is added to the total each year, so you earn interest on interest.
- Use amount equals principal x multiplier to the power of the number of years.
- The multiplier is 1 plus rate/100 for growth, 1 minus rate/100 for depreciation.
- Simple interest adds the same amount every year; compound interest grows faster.
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
Practice
6 questions, marked instantly
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Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
£500 is invested at 3% compound interest per year. How much is in the account after 2 years?
A car worth £12 000 loses 10% of its value each year. What is it worth after 2 years?
£2000 is invested at 5% compound interest per year. What is it worth after 3 years?
£800 grows to £882 after 2 years of compound interest. What is the annual interest rate?
A machine bought for £5000 loses 20% of its value each year. What is it worth after 3 years?
£1000 is invested at 4% compound interest per year. How much interest has been earned after 2 years?
Avoid these
The mistakes students make most often
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 students and parents ask
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What to learn next
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