Compound interest is one of the most powerful forces in personal finance. Albert Einstein reportedly called it the “eighth wonder of the world” — and once you understand how it works, you’ll see why.
In this guide, we’ll explain compound interest step by step, show you the formula, and give you real examples of how your savings can grow dramatically over time.
What Is Compound Interest?
Compound interest is interest calculated on both your initial deposit (the principal) and the interest you’ve already earned. In other words, your interest earns interest — and this snowball effect accelerates your growth over time.
This is different from simple interest, which is only calculated on the original principal.
The Compound Interest Formula
The compound interest formula is:
A = P × (1 + r/n)^(n×t)
- A = Final amount
- P = Principal (initial deposit)
- r = Annual interest rate (as a decimal)
- n = Number of times interest compounds per year
- t = Time in years
Compound Interest Example
Let’s say you invest £10,000 at 5% annual interest, compounded monthly, for 20 years:
A = 10,000 × (1 + 0.05/12)^(12×20) = £27,126
Your £10,000 more than doubles to £27,126 — without adding a single extra penny. That extra £17,126 is pure compound interest.
How Often Does Interest Compound?
The more frequently interest compounds, the faster your money grows. Common compounding periods include:
| Compounding Frequency | Times Per Year |
|---|---|
| Annually | 1 |
| Quarterly | 4 |
| Monthly | 12 |
| Daily | 365 |
Daily compounding gives slightly better returns than annual, though the difference narrows over shorter time periods.
The Power of Starting Early
Time is the single most important factor in compound interest. Starting just 10 years earlier can more than double your final balance.
- Invest £5,000 at age 25 at 7% annual return → £74,872 by age 65
- Invest £5,000 at age 35 at 7% annual return → £37,857 by age 65
Same investment, same rate — but starting 10 years earlier nearly doubles the outcome.
Calculate Compound Interest Free
Skip the formula and use our free compound interest calculator. Enter your principal, interest rate, compounding frequency, and time period to see exactly how your money will grow — with a full year-by-year breakdown.
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the principal. Compound interest is calculated on the principal plus any interest already earned, resulting in much faster growth over time.
How do I calculate compound interest monthly?
Use the formula A = P × (1 + r/12)^(12×t), where r is your annual rate and t is the number of years. Or use our compound interest calculator and set compounding to monthly.
Does compound interest work against you?
Yes — on debt. Credit cards and loans with compound interest grow your balance just as aggressively as savings. This is why paying off high-interest debt quickly is so important.