What Is Compound Interest?
Compound interest is interest calculated not just on your original amount (the principal), but also on the interest that has already accumulated. In plain terms: you earn interest on your interest. Over time, this creates an exponential growth effect — often called the "snowball effect" of money.
It's one of the most important financial concepts to understand, both for growing savings and for managing debt — because it works powerfully in both directions.
The Compound Interest Formula
The standard formula is:
A = P (1 + r/n)^(nt)
- A = Final amount (principal + interest)
- P = Principal (starting amount)
- r = Annual interest rate (as a decimal — e.g., 5% = 0.05)
- n = Number of times interest is compounded per year
- t = Time in years
For example: £1,000 invested at 5% annual interest, compounded yearly for 10 years:
A = 1000 × (1 + 0.05/1)^(1×10) = 1000 × 1.629 = £1,629
That's £629 of growth from doing nothing but leaving money alone.
Compounding Frequency Matters
The more often interest compounds, the more you earn. Here's what £1,000 at 5% annual rate looks like over 10 years with different compounding frequencies:
| Compounding Frequency | Final Amount |
|---|---|
| Annually | £1,628.89 |
| Quarterly | £1,643.62 |
| Monthly | £1,647.01 |
| Daily | £1,648.66 |
The differences are small at this scale, but they become significant with larger sums over longer periods.
The Rule of 72
A simple mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money.
- At 4% interest: 72 ÷ 4 = 18 years to double
- At 6% interest: 72 ÷ 6 = 12 years to double
- At 9% interest: 72 ÷ 9 = 8 years to double
This rule is an approximation, but it's remarkably accurate for rates between 2% and 15%.
Compound Interest Working Against You: Debt
The same mechanism that grows your savings can rapidly increase your debt. Credit cards, payday loans, and some personal loans use compound interest. If you carry a balance on a credit card with a high annual percentage rate (APR), the interest compounds on the unpaid balance — meaning your debt can grow quickly even if you're making minimum payments.
Key takeaway: paying off high-interest debt is mathematically equivalent to earning a guaranteed return equal to that interest rate.
How to Make Compound Interest Work for You
- Start early — time is the most powerful variable. Starting 10 years earlier can double your final amount.
- Reinvest returns — don't withdraw interest or dividends; let them compound.
- Be consistent — regular contributions amplify the compounding effect significantly.
- Minimize fees — investment fees reduce your effective rate and compound in reverse.
- Pay down high-interest debt first — no investment reliably beats the guaranteed "return" of eliminating 20%+ APR debt.
Simple vs. Compound Interest
For completeness: simple interest is only calculated on the original principal, never on accumulated interest. A £1,000 loan at 5% simple interest for 10 years means you pay £50/year in interest — £500 total. With compound interest, you'd pay £629 (if compounded annually). The difference widens dramatically over longer periods and higher rates.
Understanding this distinction is essential when evaluating savings accounts, loans, mortgages, and investments.