How Compound Interest Works: Formula, Examples & Calculator Guide
By Alex van den Berg · Updated April 2026 · 15 min read
Key Takeaway
Compound interest earns interest on previously earned interest — not just the original deposit. On £10,000 at 5% for 30 years, simple interest returns £25,000. Compound interest returns £43,219. The same mechanism that multiplies savings also multiplies debt: a £3,000 credit card balance at 22.9% APR, paid at minimum, costs over £2,000 in interest alone.
What Is Compound Interest?
Compound interest is interest calculated on both the original principal and on all accumulated interest from prior periods. The critical distinction from simple interest is that your interest earns interest — creating exponential rather than linear growth.
Consider a simple example. You deposit £1,000 at 10% annual interest.
- 1 Year 1: You earn 10% of £1,000 = £100. Balance: £1,100.
- 2 Year 2: You earn 10% of £1,100 = £110. Balance: £1,210.
- 3 Year 3: You earn 10% of £1,210 = £121. Balance: £1,331.
- 10 Year 10: Balance: £2,594 — more than double, despite a "mere" 10% rate.
With simple interest, Year 2 interest would still be £100 (always 10% of the original £1,000). You'd have exactly £2,000 at Year 10. Compounding delivers £594 more — from the same deposit at the same rate.
The Compound Interest Formula
The standard formula for compound interest is:
| Variable | Meaning | Example value |
|---|---|---|
| A | Final amount (principal + all interest) | What we're solving for |
| P | Principal — the initial deposit or loan | £10,000 |
| r | Annual interest rate as a decimal | 0.05 (= 5%) |
| n | Compounding frequency per year | 12 (monthly) |
| t | Time in years | 10 |
To find just the interest earned (not the total balance), subtract the principal: Interest = A − P.
Step-by-Step Worked Examples
Example 1 — Savings Account
Scenario: You deposit £10,000 at 5% annual interest, compounded monthly, for 10 years.
P = £10,000 · r = 0.05 · n = 12 · t = 10
A = 10,000 × (1.004167)^120
A = 10,000 × 1.64701
A = £16,470.09
Interest earned: £16,470 − £10,000 = £6,470
Simple interest at the same rate would have earned: 10,000 × 0.05 × 10 = £5,000
Compounding earns you £1,470 more — from no additional deposits.
Example 2 — Long-Term Investment
Scenario: You invest £5,000 at 7% annual interest, compounded annually, for 25 years.
P = £5,000 · r = 0.07 · n = 1 · t = 25
A = 5,000 × (1.07)^25
A = 5,000 × 5.4274
A = £27,137
Your original £5,000 grows to over £27,000 — more than 5× — without a single additional deposit. Simple interest over 25 years at 7% would produce only: 5,000 + (5,000 × 0.07 × 25) = £13,750. Compounding adds nearly £13,400 extra.
Example 3 — Credit Card Debt (Compounding Working Against You)
Scenario: You carry a £3,000 credit card balance at 22.9% APR, compounded daily (n=365), for 3 years with no repayments.
A = 3,000 × (1.000627)^1095
A = 3,000 × 1.9727
A = £5,918
A £3,000 balance grows to nearly £5,918 in 3 years with no repayments. That's £2,918 in interest — almost doubling the original debt. This is why the minimum-payment trap is so dangerous: you're paying interest on interest.
How Compounding Frequency Affects Growth
The more frequently interest compounds, the more you earn — because each cycle adds to the base on which the next cycle calculates. However, the marginal gain decreases as frequency increases: the jump from annual to monthly is large; monthly to daily is small.
| Compounding Frequency | n | After 5 yrs | After 10 yrs | After 20 yrs | After 30 yrs |
|---|---|---|---|---|---|
| Simple Interest | — | £12,500 | £15,000 | £20,000 | £25,000 |
| Annual (n=1) | 1 | £12,763 | £16,289 | £26,533 | £43,219 |
| Semi-annual (n=2) | 2 | £12,801 | £16,386 | £26,851 | £43,998 |
| Quarterly (n=4) | 4 | £12,820 | £16,436 | £27,015 | £44,402 |
| Monthly (n=12) | 12 | £12,834 | £16,470 | £27,126 | £44,677 |
| Daily (n=365) | 365 | £12,840 | £16,487 | £27,179 | £44,812 |
Based on £10,000 at 5% annual rate. Monthly highlighted as the most common bank compounding period.
💡 Practical insight: The difference between monthly (£44,677) and daily (£44,812) compounding over 30 years is just £135. Don't agonise over compounding frequency — focus on the rate, the time period, and regular additional contributions instead.
Simple Interest vs Compound Interest: The Long View
The difference between simple and compound interest is negligible over a few months — but becomes dramatic over decades. Here's how £10,000 grows at 5% under both methods:
£10,000 at 5% — Simple vs Compound (Annual)
The Rule of 72: Estimate Doubling Time Instantly
The Rule of 72 is a mental shortcut that lets you estimate — without a calculator — how long it takes to double your money at a given compound interest rate:
| Annual Rate | Rule of 72 Estimate | Actual Years | Real-World Example |
|---|---|---|---|
| 1% | 72 years | 69.7 years | Basic cash savings account |
| 2% | 36 years | 35.0 years | Premium savings bond |
| 4% | 18 years | 17.7 years | Cautious balanced fund |
| 6% | 12 years | 11.9 years | Conservative equity fund |
| 8% | 9 years | 9.0 years | Historical S&P 500 average (real) |
| 10% | 7.2 years | 7.3 years | Higher-growth portfolio |
| 18% | 4 years | 4.2 years | Typical store card APR |
| 24% | 3 years | 3.2 years | High-rate credit card |
⚠️ The Rule works in reverse for debt: At 24% APR, your unpaid debt doubles in roughly 3 years. A credit card balance of £2,000 becomes £4,000 in 3 years with no repayments. This is why paying off high-interest debt is always the highest guaranteed return available to most people.
The Power of Starting Early
Time is the dominant variable in compound interest. A 10-year headstart can produce more wealth than doubling your monthly contribution. Here's the concrete comparison for monthly ISA/pension contributions at 7% average annual return:
| Investor | Starts at | Monthly Contribution | Total Contributed | Value at 65 | Compound Gain |
|---|---|---|---|---|---|
| Early starter | Age 25 | £300/month | £144,000 | £760,000 | +£616,000 |
| Late starter | Age 35 | £300/month | £108,000 | £378,000 | +£270,000 |
| Late + higher | Age 35 | £600/month | £216,000 | £756,000 | +£540,000 |
Assumes 7% annual return compounded monthly. Figures are illustrative and do not account for tax or inflation.
The late starter who contributes twice as much (£600/month vs £300) still barely matches the early starter. The 10-year headstart, in this scenario, is worth roughly the same as doubling your monthly saving for 30 years.
💡 The practical rule: The best time to start investing was 10 years ago. The second best time is today. Even small amounts — £50 or £100 per month — started early compound into significant sums over a working lifetime.
APR vs APY: Which One Tells the Truth?
Banks and lenders present interest in two ways — and choosing which to display is not accidental:
- APR (Annual Percentage Rate) — the stated rate, without accounting for compounding frequency. Used on loan advertisements because it sounds lower.
- APY (Annual Percentage Yield) — the effective annual rate after compounding is factored in. Used on savings accounts because it sounds higher.
A 5% APR compounded monthly has an APY of:
APY = (1 + 0.05/12)^12 − 1 = (1.004167)^12 − 1 = 5.116%
A 5% APR compounded daily has an APY of:
APY = (1 + 0.05/365)^365 − 1 = 5.127%
The difference is small — but when comparing mortgage offers or savings accounts, always convert to APY for a fair comparison.
How Inflation Affects Compound Growth
Inflation silently erodes the purchasing power of your growing balance. To find your real compound growth rate, use the Fisher equation:
If your ISA returns 5% but inflation runs at 3%, your real return is approximately 2%. Your balance grows in numbers but its purchasing power grows only at 2%. This is why long-term savings held only in cash accounts — which typically yield 1–4% — frequently fail to maintain real value over decades.
5 Ways to Maximise Compound Growth
Compound Interest FAQ
Calculate Your Compound Growth
Enter your starting balance, monthly contribution, interest rate, and time period to see exactly how your money grows.
Related Articles
Alex van den Berg
Financial Educator & Mathematics Writer
Alex has 8+ years of experience in personal finance education and mathematics instruction. He writes practical guides on financial calculations, everyday maths, and how to use digital tools to make smarter money decisions.