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Compound interest is the process where the interest you earn each period is added to your principal, so that from that moment on, the interest is earned on both the principal and the previously accumulated interest. In simple terms: you earn interest on your interest.
Albert Einstein reportedly called compound interest "the eighth wonder of the world," saying: "He who understands it, earns it; he who doesn't, pays it." Whether or not he actually said it, the math speaks for itself.
The standard formula for compound interest (lump sum, no additional contributions) is:
FV = PV × (1 + r/n)n×t
Where:
PV = Present Value (initial investment)
r = Annual interest rate (decimal)
n = Compounding frequency per year
t = Time in years
When you make regular monthly contributions, the formula becomes more powerful — each contribution starts compounding from the moment it's made, meaning earlier contributions have more time to grow.
The difference is dramatic over long periods. Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all accumulated interest.
Example: $10,000 invested at 8% for 30 years:
That's nearly 3× more — and the gap widens the longer your time horizon.
The more frequently interest is compounded, the more you earn. Here's how $10,000 at 8% grows in 20 years under different compounding frequencies:
Daily compounding beats annual compounding by about 6% over 20 years. The difference is modest but real — and it adds up with larger balances.
A quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money.
Examples:
At 6% → 72 ÷ 6 = 12 years to double
At 8% → 72 ÷ 8 = 9 years to double
At 10% → 72 ÷ 10 = 7.2 years to double
The Rule of 72 is surprisingly accurate for interest rates between 4% and 12%.
Most people build wealth through regular contributions, not lump sums. Investing $500/month for 30 years at 8% grows to approximately $745,000 — even though you only "put in" $180,000. The remaining $565,000 is pure compounding.
This is why automated investing (like 401k contributions or automatic transfers to an index fund) is so effective — it's not about timing the market, it's about time in the market.
A nominal future value of $1 million sounds great — until you adjust for inflation. At 3% annual inflation, $1 million in 30 years has the purchasing power of roughly $412,000 in today's dollars.
This is why your investments need to outpace inflation. A savings account earning 1% when inflation is 3% means you're effectively losing 2% of purchasing power every year.