Understanding Compound Interest

Compound interest is interest calculated on both the initial principal and accumulated interest from previous periods. Often called "interest on interest," it's the key to building wealth over time.

**Simple Interest**: Calculated only on principal amount.

**Compound Interest**: Calculated on principal plus accumulated interest.

The difference becomes dramatic over time, making compound interest Einstein's alleged "eighth wonder of the world."

The fundamental formula for compound interest:

**A = P(1 + r/n)^(nt)**

Where: - A = Final amount - P = Principal (initial investment) - r = Annual interest rate (decimal) - n = Number of times interest compounds per year - t = Time in years

Example: $10,000 at 7% for 10 years, compounded monthly A = 10,000(1 + 0.07/12)^(12×10) = $20,096.61

How often interest compounds significantly affects growth:

**Annual Compounding**: Interest added once per year **Semi-Annual**: Twice per year **Quarterly**: Four times per year **Monthly**: Twelve times per year **Daily**: 365 times per year **Continuous**: Mathematical limit of infinite compounding

More frequent compounding yields higher returns. The difference between monthly and annual compounding can be thousands of dollars over time.

A quick way to estimate doubling time:

**Years to Double = 72 ÷ Interest Rate**

Examples: - 6% interest: 72 ÷ 6 = 12 years to double - 9% interest: 72 ÷ 9 = 8 years to double - 12% interest: 72 ÷ 12 = 6 years to double

This rule helps quickly assess investment potential without complex calculations.

Real-world applications:

**Retirement Accounts**: 401(k)s and IRAs harness compound interest for decades.

**Savings Accounts**: Even modest rates compound over time.

**Credit Card Debt**: Compound interest works against you with high rates.

**Mortgages**: Front-loaded interest means early extra payments have huge impact.

Starting early is crucial - time is the most powerful factor in compounding.