Interest is the cost of borrowing money or the reward for saving it. But not all interest is calculated the same way. Simple interest and compound interest produce very different results over time, and understanding which type applies to your savings account, loan, or investment can make a significant difference to your financial outcomes.
Simple Interest
Simple interest is calculated only on the original principal — it never earns interest on itself. The formula is straightforward:
Simple Interest = P × r × t
Total = P + (P × r × t) = P(1 + rt)
- P = Principal
- r = Annual interest rate (decimal)
- t = Time in years
Example:
£10,000 invested at 5% simple interest for 10 years:
Interest = £10,000 × 0.05 × 10 = £5,000
Total = £10,000 + £5,000 = £15,000
Note that the interest earned is exactly the same each year: £500. The "line" of growth is perfectly straight.
Compound Interest
Compound interest earns interest on both the principal AND accumulated interest from previous periods. The formula is:
A = P(1 + r/n)nt
Same example with annual compounding:
£10,000 at 5% compounded annually for 10 years:
A = £10,000 × (1.05)10 = £10,000 × 1.6289 = £16,289
Interest earned = £16,289 − £10,000 = £6,289 vs £5,000 simple interest — a difference of £1,289 from the same principal and rate.
The Growing Gap Over Time
The real power of compound interest only becomes apparent over long periods. Here's the same £10,000 at 5% over different time horizons:
| Years | Simple Interest (£) | Compound Interest (£) | Difference (£) |
|---|---|---|---|
| 5 | 12,500 | 12,763 | 263 |
| 10 | 15,000 | 16,289 | 1,289 |
| 20 | 20,000 | 26,533 | 6,533 |
| 30 | 25,000 | 43,219 | 18,219 |
| 40 | 30,000 | 70,400 | 40,400 |
| 50 | 35,000 | 114,674 | 79,674 |
After 50 years, compound interest produces more than three times the simple interest result. The growth curve is exponential vs linear.
Where Each Type Is Used
Simple Interest
- Short-term loans (payday lenders often quote simple daily rates)
- Some car loans (flat-rate car finance)
- Treasury bills and some government bonds
- Interest calculations in some legal contexts
- Quick estimation when precision isn't critical
Compound Interest
- Bank savings accounts (compounded daily or monthly)
- ISAs and investment accounts
- Mortgages and personal loans (technically amortised, but interest compounds daily on the outstanding balance)
- Credit cards (interest compounds daily in most cases)
- Pensions and long-term investments
The Frequency Effect
Compound interest grows faster when compounding occurs more frequently. Comparing £10,000 at 5% over 10 years:
| Compounding Frequency | Final Amount |
|---|---|
| Annual | £16,289 |
| Quarterly | £16,436 |
| Monthly | £16,470 |
| Daily | £16,487 |
| Continuous | £16,487 |
The gains from higher frequency diminish rapidly — going from annual to daily compounding adds only £198 over 10 years. Rate and time are far more impactful than compounding frequency.
Effective Annual Rate (EAR)
To compare accounts with different compounding frequencies, convert to EAR (also called AER in the UK):
EAR = (1 + r/n)n − 1
A 5% nominal rate compounded monthly: EAR = (1 + 0.05/12)12 − 1 = 1.0512 − 1 = 5.12% AER
UK savings accounts must by law display their AER, making fair comparison straightforward. Always compare AER when choosing savings products.
Compound Interest Working Against You
On credit cards charging 22.9% APR (a common rate), interest compounds daily. A £3,000 balance left unpaid for one year doesn't cost just £687 (£3,000 × 22.9%) — it costs closer to £767 due to daily compounding. This is why only paying the minimum on credit cards keeps many people in debt for years.
Summary
Simple interest grows linearly (same amount each period); compound interest grows exponentially (interest on interest). Over short periods, the difference is small. Over 20+ years, it's enormous. Savings accounts, ISAs, and mortgages use compound interest. The earlier you start saving and the longer you hold, the more exponential growth works in your favour.