Albert Einstein allegedly called compound interest "the eighth wonder of the world." Whether or not he said it, the principle is real: money earns returns, those returns earn returns, and over long periods the growth becomes extraordinary.
The Compound Interest Formula
A = P × (1 + r/n)^(n×t)
Where A = final amount, P = principal (starting amount), r = annual interest rate (as a decimal), n = number of compounding periods per year, t = number of years.
Example: £10,000 invested at 7% per year, compounded annually for 20 years: A = 10,000 × (1.07)^20 = £38,697. You invested £10,000 and ended with £38,697 — £28,697 in interest from doing nothing except waiting.
The Rule of 72
Divide 72 by the annual interest rate to find roughly how many years it takes to double your money. At 6%, money doubles in 12 years (72 ÷ 6). At 9%, 8 years. At 12%, 6 years. This mental shortcut works well for rates between 4% and 15% and is one of the most useful rules in personal finance.
Why Starting Early Matters So Much
This is where compound interest becomes truly compelling. Consider two investors, both earning 8% per year:
- Early Investor: Invests £5,000/year from age 25 to 35, then stops. Total invested: £50,000.
- Late Investor: Invests £5,000/year from age 35 to 65. Total invested: £150,000.
At age 65, the Early Investor has approximately £615,000 and the Late Investor has approximately £565,000 — despite the Early Investor putting in £100,000 less. Starting 10 years earlier, then stopping, beats contributing for 30 years but starting late. Time is the most powerful variable.
Simple Interest vs Compound Interest
Simple interest applies the rate only to the original principal each period. Compound interest applies the rate to the growing balance including accumulated interest. On £10,000 at 7% over 20 years: simple interest = £14,000 in interest; compound interest = £28,697 in interest — more than double.
How Compounding Frequency Affects Growth
More frequent compounding produces more growth, though the difference between daily and monthly compounding is small in practice. £10,000 at 5% for 10 years: annually = £16,289; monthly = £16,470; daily = £16,487. The annual vs monthly gap (£181) matters more for larger amounts or longer timeframes.
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