What is Compound Interest? The Power of Compounding Explained
Understand compound interest, how it differs from simple interest, the formula, and why Einstein called it the 8th wonder of the world.
What is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. In simple terms: your money earns interest on its interest.
The Formula
A = P × (1 + r/n)^(n×t)
- A = Final amount
- P = Principal (initial investment)
- r = Annual interest rate (decimal)
- n = Number of times interest compounds per year
- t = Time in years
Compound vs Simple Interest
Simple interest: Interest is only calculated on the original principal. Formula: P × r × t
Compound interest: Interest is calculated on principal + accumulated interest. Grows exponentially.
Example: £10,000 at 7% for 30 years:
- Simple interest: £31,000 total
- Compound interest (annual): £76,123 total
That's a £45,000 difference — the power of compounding.
How Compounding Frequency Matters
The more frequently interest compounds, the more you earn:
- Annually: £10,000 → £19,672 (10 years at 7%)
- Monthly: £10,000 → £20,097
- Daily: £10,000 → £20,138
The Rule of 72
A quick way to estimate how long your money takes to double: divide 72 by the interest rate. At 7%, your money doubles in approximately 72 ÷ 7 = 10.3 years.
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