Compound Interest
Interest earned on principal and past interest.
Key idea
Interest earned on principal and past interest.
In depth
With compound interest, earned interest is added to the principal and then earns interest itself, so growth accelerates: A = P(1 + r/n)^(nt). The more often it compounds, the more you earn, with an upper limit set by the number e.
Worked example
1,000 at 5% for 3 years compounded yearly: 1000 × 1.05³ = 1157.63, compared with 1150 for simple interest.
Formula
Real-world uses
- Growing savings in pensions and ISAs
- Comparing credit card debt growth
- Planning long-term investments
Common mistake
Using the formula with r as a percent (5) instead of a decimal (0.05).
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Compound Interest?
Interest earned on principal and past interest. It is a topic at the advanced level in Arithmetic & Number Sense.
What is the formula for Compound Interest?
The key formula is A = P(1 + r/n)^(nt).
Where is Compound Interest used in real life?
Real-world examples: Growing savings in pensions and ISAs; Comparing credit card debt growth; Planning long-term investments.
What should I learn before Compound Interest?
Make sure you are comfortable with Simple Interest, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Compound Interest?
Using the formula with r as a percent (5) instead of a decimal (0.05).
How can I practise Compound Interest?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Compound Interest?
Move on to Ratios next.
Related advanced topics in Arithmetic & Number Sense
- Repeating Decimals – Decimals with a repeating block are rational and convertible to fractions.
- Inverse Proportion – When one quantity doubles, the other halves.
- Rational Numbers – Numbers expressible as p/q with integers p, q, q≠0.
- Irrational Numbers – Real numbers that cannot be written as a fraction, such as √2 and π.
- Real Numbers – All rational and irrational numbers; the continuous number line.
- Square Roots of Non-squares – Approximate or simplify surds like √50 = 5√2.