Free Guide

How Compound Interest Works
(With Calculator)

Compound interest is one of the most powerful forces in personal finance. This guide explains exactly how it works, shows you the maths, and lets you calculate your own numbers instantly.

Contents

  1. What is compound interest?
  2. The compound interest formula
  3. A simple example
  4. Daily vs monthly vs yearly compounding
  5. The Rule of 72
  6. Common mistakes to avoid
  7. Try it yourself

What is Compound Interest?

Compound interest is interest calculated on both your original principal and the interest already earned. This is different from simple interest, which only ever calculates on the original amount.

The result is exponential growth — your money grows faster and faster over time, because each period's interest becomes part of the base for the next period's calculation. This is what Einstein reputedly called "the eighth wonder of the world."

💡 Simple interest on £1,000 at 10%/yr for 3 years = £300 total interest.
Compound interest on the same = £331 — and the gap grows every year.

The Compound Interest Formula

The standard formula is:

A = P × (1 + r/n) ^ (n × t)
  • A — Final amount (principal + interest)
  • P — Principal (your starting amount)
  • r — Annual interest rate (as a decimal, e.g. 5% = 0.05)
  • n — Number of times interest compounds per year
  • t — Time in years

If you're compounding once per year, the formula simplifies to: A = P × (1 + r) ^ t

A Simple Example

You invest £5,000 at an annual interest rate of 7%, compounding yearly, for 10 years.

A = 5000 × (1 + 0.07) ^ 10 = £9,836

You started with £5,000. You end with £9,836 — nearly double, without adding a single extra penny. The £4,836 of interest came purely from compounding.

💡 With simple interest at the same rate, you'd have earned only £3,500 interest — £1,336 less.

Daily vs Monthly vs Yearly Compounding

The more frequently interest compounds, the more you earn. Here's £10,000 at 5% over 10 years with different compounding periods:

CompoundingFinal BalanceInterest Earned
Yearly£16,289£6,289
Monthly£16,470£6,470
Daily£16,487£6,487

The difference between daily and yearly compounding is relatively small at typical savings rates. What matters far more is time and rate.

The Rule of 72

The Rule of 72 is a quick mental shortcut to estimate how long it takes to double your money with compound interest.

Years to double = 72 ÷ annual interest rate (%)
  • At 6%/yr → doubles in ~12 years
  • At 8%/yr → doubles in ~9 years
  • At 12%/yr → doubles in ~6 years
💡 The Rule of 72 works in reverse too — divide 72 by the years to find what rate you need to double your money in that time.

Common Mistakes to Avoid

Waiting to start

Every year you delay is exponentially more costly than you think. The early years of compounding build the base for everything that follows.

Ignoring fees

A 1% annual management fee sounds tiny. Over 30 years it can consume 20–25% of your final balance. Always check charges.

Withdrawing early

Taking money out resets the snowball effect. Even a single withdrawal can cost years of compounded gains.

Only looking at the rate

A higher rate matters less than you think if the time horizon is short. Time × rate together is what creates wealth.

Try It Yourself

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