A — Final amount (principal + interest)
P — Principal (starting amount)
r — Annual interest rate as a decimal (e.g. 8% = 0.08)
n — Number of times interest compounds per year (1 = annual, 12 = monthly, 365 = daily)
t — Time in years

Worked example — annual compounding

You invest £10,000 at 8% per year, compounded annually for 20 years:

A = 10,000 × (1 + 0.08/1)^1×20
A = 10,000 × (1.08)²⁰
A = 10,000 × 4.661 = £46,610

Your £10,000 grew to over £46,000 — without adding another penny.

Worked example — monthly compounding

Same £10,000 at 8%, but compounded monthly (n = 12) for 20 years:

A = 10,000 × (1 + 0.08/12)^12×20
A = 10,000 × (1.00667)²⁴⁰
A ≈ £49,268

Monthly compounding adds an extra ~£2,658 vs annual compounding over 20 years.

The Rule of 72

A quick mental shortcut: divide 72 by your interest rate to estimate how many years to double your money. At 8% → 72 ÷ 8 = 9 years to double. At 6% → 12 years. Works well for rates between 5–15%.

Why compound interest is so powerful

With compound interest, you earn interest on your previous interest. This creates exponential — not linear — growth. The longer the timeframe, the more dramatic the effect. Starting 10 years earlier can double your final amount.

Frequently asked questions

What is the difference between simple and compound interest?
Simple interest is always calculated on the original principal. Compound interest is calculated on the growing balance. Over time, compound interest grows dramatically faster.

Does compounding frequency matter a lot?
For typical investment rates, the difference between monthly and daily compounding is small. What matters most is the interest rate and investment duration.

How does inflation affect compound interest?
Inflation erodes purchasing power. If your investment earns 7% but inflation runs at 3%, your real return is approximately 4%. Always consider real (inflation-adjusted) returns for long-term planning.