Simple Interest and Compound Interest
Simple interest is worked out only on the original amount, so you earn the same each year. On £100 at 5% that is £5 a year. Compound interest also pays interest on the interest already added, so your money grows faster.
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How to Calculate Simple Interest?
- Interest = Principal × rate × time, calculated on the original amount only.
- The total amount = Principal + Interest, since the principal stays the same each year.
How to Calculate Compound Interest?
- The total amount is calculated using Principal × (1 + rate)ᵗ.
- Interest is added to the principal each year, so the amount keeps increasing.
- The interest is calculated using Interest = Total − Principal.
Simple and Compound Compared
- Simple interest increases by the same amount each year.
- Compound interest increases faster over time because interest is added to the total.
- Compound interest is commonly used by banks.
Practice Questions
Test your understanding
You invest £200 in a bank offering simple interest annually. How much total interest will you earn after 5 years?
Correct! 🎉 +10 pointsNot quite right
The principal is £200, and the annual interest is £8. For 5 years, multiply the yearly interest by the number of years: £ £40.
A bank offers a annual simple interest rate. If you invest £300 for 3 years, how much total interest will you earn?
Correct! 🎉 +10 pointsNot quite right
The principal is £300, and the interest for 1 year is £ £12. For 3 years, multiply the 1-year interest by 3: £ £36.
You invest £500 in a bank that offers compound interest annually. How much total amount will you have after 2 years?
Correct! 🎉 +20 pointsNot quite right
Compound interest means the total amount after 2 years is calculated as £500 × (1 + )². First year: £ £525. Second year: £ £551.25.
A bank offers a annual simple interest rate. How much interest would you earn on a £1000 investment over 4 years, and what would the total amount be?
Correct! 🎉 +20 pointsNot quite right
The interest for 1 year is £ £50. For 4 years, multiply the 1-year interest by 4: £ £200. Add the interest to the principal: £1000 + £ £1200.
You deposit £500 in a bank offering a annual simple interest rate. How much total amount will you have after 4 years?
Correct! 🎉 +20 pointsNot quite right
The principal is £500, and the annual interest is £ £30. For 4 years, multiply the 1-year interest by 4: £ £120. Add the interest to the principal: £500 + £ £620.
You invest £200 in a bank offering a annual compound interest rate. How much total amount will you have after 2 years?
Correct! 🎉 +30 pointsNot quite right
Use the compound interest formula: Total Amount = Principal × (1 + Interest Rate)ⁿ. After 1 year: £ £210. After 2 years: £ £220.5.
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Interactive Activity
Compare how simple interest and compound interest grow your money over time
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Students Also Ask
The questions students bump into most on this topic
Simple interest is worked out only on your original amount, so you earn the same amount every year. Compound interest is worked out on your original amount plus the interest already added. Your balance therefore grows faster each year. Over the same period, compound interest usually earns more.
Compound interest pays interest on the interest you have already earned, not just on your original amount. Each year that interest is added to your balance, so the next year you earn interest on a larger amount. Simple interest only ever uses the original amount, so it grows more slowly.
With compound interest, the interest you earn each year is added to your balance. That new total becomes the principal for the next year. So the following year's interest is worked out on a larger amount. Your money grows by a little more each year.
Compound interest is more common in real life. Most savings accounts and loans add interest to the running balance. You then earn or pay interest on that interest too. Simple interest is mainly a quick way to estimate interest over several years.
The total amount equals the principal times (1 plus the interest rate), to the power of the number of years. Written in symbols: total = P x (1 + r) to the power of n. Subtract the original principal to find the interest earned.