Simple vs Compound Interest: What's the Difference?
A complete comparison of simple and compound interest — with formulas, a side-by-side worked example, a compounding frequency table, and when each applies in real life.
The Two Formulas
A = P × (1 + r × t)
Where P = principal, r = annual rate (decimal), t = time in years.
Interest is calculated only on the original principal. It does not grow.
Where n = compounding periods per year.
Interest is added to the principal, then earns interest itself. It grows exponentially.
Side-by-Side Worked Example
£5,000 invested at 6% per year for 10 years.
Simple: A = 5,000 × (1 + 0.06 × 10) = 5,000 × 1.6 = £8,000 (interest: £3,000)
Compound (annual, n=1): A = 5,000 × (1.06)10 = 5,000 × 1.7908 = £8,954 (interest: £3,954)
Compound (monthly, n=12): A = 5,000 × (1.005)120 = 5,000 × 1.8194 = £9,097 (interest: £4,097)
Compound (daily, n=365): A ≈ 5,000 × 1.8220 = £9,110 (interest: £4,110)
Simple: A = 5,000 × (1 + 1.8) = £14,000 (interest: £9,000)
Compound (annual): A = 5,000 × (1.06)30 = 5,000 × 5.7435 = £28,717 (interest: £23,717)
Compound (monthly): A = 5,000 × (1.005)360 = 5,000 × 6.023 = £30,115 (interest: £25,115)
Over 30 years, compound monthly interest generates £16,115 more than simple interest on the same £5,000 at 6%. The gap widens with time — this is the exponential nature of compounding.
Compounding Frequency Table
The more often interest compounds, the more you earn. Here is how different compounding frequencies affect a £5,000 deposit at 6% over 10 years.
| Frequency | n | Total after 10 yr | Interest earned |
|---|---|---|---|
| Annual | 1 | £8,954 | £3,954 |
| Quarterly | 4 | £9,070 | £4,070 |
| Monthly | 12 | £9,097 | £4,097 |
| Daily | 365 | £9,110 | £4,110 |
| Continuous | ∞ | £9,111 | £4,111 |
Continuous compounding (A = Pert): A = 5,000 × e0.6 = £9,111. The difference between monthly and continuous compounding is negligible in practice (£14 on £5,000 over 10 years). See the compound interest formula →
Where Each Type Is Used
- Short-term personal loans and car finance (some)
- Government savings bonds (fixed return over fixed term)
- Bridging loans
- Trade credit between businesses
- Treasury bills
Simple interest is predictable and easy to verify: total interest = P × r × t regardless of when it is paid.
- Savings accounts and cash ISAs (compounds monthly or daily)
- Investment returns over time (dividends reinvested)
- Mortgages (interest calculated on remaining balance monthly)
- Credit card debt (compounds daily — works against you)
- Pensions and stocks and shares ISAs
Compound interest is standard wherever the balance changes over time.
Which Is Better?
It depends which side of the transaction you are on:
Earning: compound interest is always better — your returns earn returns.
Borrowing: simple interest is better — the total owed is fixed and transparent.
Credit cards compound daily and can turn a £1,000 balance into over £1,200 in a year at 20% APR if only minimum payments are made. The same compounding that builds wealth in savings works against you in debt.
Calculate compound interest for your specific amount and rate
Open Compound Interest Calculator →Frequently Asked Questions
What is the main difference between simple and compound interest?
Simple interest is calculated only on the original principal (I = P × r × t); the amount never earns interest on itself. Compound interest adds earned interest back to the principal each period, so future interest is calculated on a growing balance. Over long periods, the difference is dramatic — compound interest grows exponentially, simple interest grows linearly.
Which type of interest do savings accounts use?
Virtually all modern savings accounts, ISAs, and investment accounts use compound interest. Interest is typically calculated daily and credited monthly. This means your balance earns interest on previously credited interest every month, accelerating growth. Check the AER (Annual Equivalent Rate) to compare accounts — AER always assumes compounding.
Does APR vs AER matter for comparing compound interest?
Yes. APR (Annual Percentage Rate) on borrowing shows the nominal rate; AER (Annual Equivalent Rate) on savings shows the effective rate after compounding. If a savings account pays 6% AER with monthly compounding, the monthly rate is 0.5% — but the AER correctly shows the total annual return as 6.17% ((1.005)12 − 1). AER makes it easier to compare accounts with different compounding frequencies.
How does compound interest apply to debt?
Compound interest on debt works the same way but in reverse: unpaid interest is added to the balance, and future interest accrues on the higher total. Credit cards typically compound daily. A £1,000 balance at 20% APR compounds to roughly £1,221 after one year if no payments are made — interest alone adds £221, and the process accelerates with each passing month. Paying more than the minimum is essential to prevent this.
Evidence & Methodology
How This Page Is Grounded
Method
Compares principal × rate × time with compound growth over the same principal, rate and duration.
Important limitation: Examples use fixed rates and do not include fees, tax, inflation or changing balances unless stated.
Primary Sources
- Compound interest Investor.gov — U.S. Securities and Exchange Commission
Quality Checks
Worked examples are checked at one period, multiple periods and zero rate.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.