How to Calculate Compound Interest
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Compound interest is one of the most useful concepts in finance because it shows how money can grow on top of previous growth. This guide explains the formula, the logic behind it, and how to work out compound interest step by step.
The compound interest formula
A = P(1 + r/n)nt
- A = final amount
- P = starting principal
- r = annual interest rate as a decimal
- n = number of compounding periods per year
- t = time in years
This formula works because each compounding period increases the balance, and the next period then uses that higher balance.
Step-by-step method
- Write down the starting amount.
- Convert the annual rate into decimal form. For example, 5% becomes 0.05.
- Choose the compounding frequency. Monthly compounding means 12 periods per year.
- Multiply the number of years by the number of periods per year.
- Apply the formula and subtract the original principal if you want interest earned only.
Worked example
Suppose you invest £1,000 at 5% annual interest for 10 years, compounded monthly.
Using the formula, the ending balance is approximately £1,647.01. The interest earned is therefore about £647.01.
Simple interest vs compound interest
With simple interest, you earn interest only on the original amount. With compound interest, you also earn interest on past interest. That means the gap between the two methods usually widens over time.
Try both with our Simple Interest Calculator and Compound Interest Calculator.
Practical uses
- Savings account projections
- Investment growth planning
- Pension estimates
- Long-term wealth building comparisons
- Education and homework support
FAQ
What is the formula for compound interest?
The core formula is A = P(1 + r/n)^(nt), where P is principal, r is annual rate, n is compounding periods per year, and t is time in years.
Why does compound interest grow faster than simple interest?
Because each period adds interest to the balance, and later interest is then calculated on that larger balance.
Is time more important than rate?
Often yes. A longer time horizon gives compounding more opportunities to work, which can be more powerful than a small increase in rate.