Compound vs Simple Interest
Simple interest grows linearly. Compound interest grows exponentially — it earns interest on interest. Over time, the difference becomes enormous, which is why compound interest is called the eighth wonder of the world.
The formulas
Simple interest: I = P × r × t (Principal × rate × time). Compound interest: A = P × (1 + r/n)^(n×t) where n is compounding frequency per year.
Real-world impact over 30 years
| Simple interest (5% p.a.) | Compound interest (5% p.a., annual) | |
|---|---|---|
| Starting amount | £10,000 | £10,000 |
| After 10 years | £15,000 | £16,289 |
| After 20 years | £20,000 | £26,533 |
| After 30 years | £25,000 | £43,219 |
Where each appears
- Simple interest: some short-term loans, certain bonds, hire-purchase agreements
- Compound interest: savings accounts, investment returns, credit card debt, mortgages
- Daily compounding (credit cards): interest accrues every day — most expensive form for borrowers
- Monthly compounding (most savings accounts): balance grows each month
For borrowers vs savers
As a saver: compound interest is your friend — start early, reinvest returns, and let time do the work. As a borrower: compound interest works against you — high-interest debt like credit cards compounds daily, making minimum payments expensive. Pay off high-rate debt before investing.
Frequently Asked Questions
Which is better for a savings account?
Compound interest is always better for savings — you earn interest on your accumulated interest, not just the original deposit.
How often should interest compound for maximum growth?
More frequent compounding means slightly more growth: daily > monthly > quarterly > annually. The differences are small for typical rates.
Does compounding frequency matter much?
At 5% p.a., daily vs annual compounding on £10,000 for 10 years: £16,487 vs £16,289 — a difference of £198. Meaningful over very long periods or large amounts.