The Power of Compound Interest
Albert Einstein famously called compound interest the eighth wonder of the world: "He who understands it, earns it; he who doesn't, pays it." Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods.
The Impact of Compounding Frequency
The more frequently interest is compounded within a given year (e.g., monthly vs. annually), the greater the effective annual return because earned interest starts generating its own interest sooner.
Mathematical Formula
Where A = Final Balance, P = Principal, r = Annual Rate (decimal), n = Compounding frequency per year, t = Years.
Step-by-Step Worked Example
Investing $5,000 at an 8% annual return compounded monthly for 10 years:
1. P = 5000, r = 0.08, n = 12, t = 10
2. r/n = 0.08 / 12 Ôëê 0.006667
3. nt = 12 × 10 = 120
4. A = 5000 ├ù (1.006667)┬╣┬▓Ôü░ = 5000 ├ù 2.2196 Ôëê $11,098.20
5. Total Interest Earned: $6,098.20.
Important Considerations & Limitations
Compound interest calculations assume consistent compounding and uninterrupted reinvestment. Real-world returns may be reduced by capital gains taxes, fund management fees, and inflation.
Authoritative References
U.S. Securities and Exchange Commission (SEC) Compound Interest Calculator & Investor Guide.