What is Compound Interest?
Compound interest is interest calculated on the initial principal plus the accumulated interest from previous periods. It is often called "interest on interest" and is the reason why long-term investing is so powerful.
The Compound Interest Formula
A = P (1 + r/n)nt + PMT × [((1 + r/n)nt − 1) / (r/n)]
Where:
- A = Final Amount
- P = Principal (initial investment)
- r = Annual interest rate (decimal)
- n = Number of times interest is compounded per year
- t = Time in years
- PMT = Regular contribution amount
Key Insights
- Compounding Frequency Matters: More frequent compounding (daily > monthly > annually) results in higher returns.
- Time is Powerful: The longer your money compounds, the more dramatic the growth becomes.
- Regular Contributions Accelerate Growth: Adding money consistently significantly boosts your final balance.
- Rule of 72: A quick way to estimate doubling time: 72 ÷ Interest Rate (%). Example: At 8%, money doubles approximately every 9 years.
Simple vs Compound Interest
With simple interest, you only earn interest on the original principal. With compound interest, you earn interest on both the principal and previously earned interest. Over long periods, the difference is enormous.