Simple and Compound Interest
Simple interest is a fixed amount of interest paid on the original amount invested, the principal, every year, so the interest earned is the same each year, while compound interest is calculated on the current balance each year, including any interest already added, so the amount earned grows each year. Compound interest over several years can be found in one calculation by raising the multiplier for the interest rate to the power of the number of years and multiplying it by the principal.
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Method
- Simple interest is calculated only on the original principal every year, so the interest earned is the same amount each year.
- To calculate simple interest, multiply the principal by the interest rate (as a decimal) and by the number of years, or find one year's interest and multiply by the number of years.
- To find the total amount after simple interest, add the total interest earned to the original principal.
- Compound interest is calculated on the current balance each year, including any interest already added, so the amount of interest earned increases each year.
- To calculate compound interest, find the multiplier for the interest rate (for example, 1.03 for 3%), then multiply the principal by this multiplier once for each year, or raise the multiplier to the power of the number of years.
- To find the compound interest earned, rather than the total amount, subtract the original principal from the final total amount.
- For a small number of years, compound interest can also be built up year by year, applying the multiplier to the previous year's total each time - useful for checking a power calculation or for showing full working.
Worked example
Nadia invests 1200 pounds in a savings account paying 3% compound interest per year. Work out the total amount in her account after 3 years, giving your answer to the nearest penny.
- Find the multiplier for a 3% increase: 1 + 0.03 = 1.03.
- Apply the multiplier once for each of the 3 years: 1200 x 1.03 x 1.03 x 1.03, or 1200 x 1.03^3.
- Calculate 1.03^3 = 1.092727.
- Multiply by the principal: 1200 x 1.092727 = 1311.2724.
- Round to the nearest penny: 1311.27 pounds.
Practice questions
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Q1Work out the simple interest earned on 900 pounds invested for 4 years at a simple interest rate of 2.5% per year.Show answer
Answer: 90 pounds (900 x 0.025 = 22.50 pounds per year, then 22.50 x 4)
Q2Kofi invests 650 pounds at a simple interest rate of 3% per year. Work out the total amount in his account after 5 years.Show answer
Answer: 747.50 pounds (interest = 650 x 0.03 x 5 = 97.50, then 650 + 97.50)
Q3A savings account pays 4% compound interest per year. Work out the total amount after 2 years if 500 pounds is invested.Show answer
Answer: 540.80 pounds (500 x 1.04 x 1.04)
Q41000 pounds is invested at a compound interest rate of 5% per year for 2 years. Work out the total compound interest earned, not the total amount.Show answer
Answer: 102.50 pounds (1000 x 1.05 x 1.05 = 1102.50, then 1102.50 - 1000)
Q51500 pounds is invested for 2 years. Option A pays 6% simple interest per year. Option B pays 5.5% compound interest per year. Work out the total amount for each option after 2 years, and state which option gives the larger total.Show answer
Answer: Option A gives 1680 pounds (1500 + 2 x 90); Option B gives 1669.54 pounds (1500 x 1.055 x 1.055); Option A gives the larger total
Q6Bilal invests 800 pounds and earns 120 pounds in simple interest after 5 years. Work out the annual simple interest rate.Show answer
Answer: 3% (120 / 5 = 24 pounds per year, then 24 / 800 x 100)
Q7A trust fund of 2000 pounds is invested at a compound interest rate of 10% per year. Work out the value of the trust fund after 3 years.Show answer
Answer: 2662 pounds (2000 x 1.1 x 1.1 x 1.1)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Priya invests 2400 pounds in a savings account that pays 3.5% compound interest per year. (a) Work out the total amount in the account after 2 years, giving your answer to the nearest penny. (b) Work out the total compound interest earned over these 2 years.
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A car bought for 18000 pounds loses value (depreciates) at a compound rate of 15% per year. (a) Work out the value of the car after 3 years, to the nearest pound. (b) A second, identical car is bought at the same time for the same price, but its value instead falls by a simple, straight-line, 15% of its original price every year. Work out the value of this second car after 3 years, and state which car is worth more after 3 years.
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Free printable worksheet
Want more practice on paper? Download the simple and compound interest worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 43 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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