Simple Interest: The Basics
Simple interest is straightforward: you earn (or pay) interest only on the original amount. It never compounds — interest doesn't earn more interest.
Interest = Principal × Rate × Time Example: $10,000 × 0.05 × 3 years = $1,500 After 3 years, your $10,000 has earned exactly $1,500 in interest regardless of how often it's calculated.
Compound Interest: The Growth Engine
Compound interest earns interest on your interest. This creates exponential growth — the longer money compounds, the faster it grows. Albert Einstein reportedly called compound interest the most powerful force in the universe.
A = P × (1 + r/n)^(n×t) A = Future Value, P = Principal r = Annual Rate, n = Compounds/Year, t = Years $10,000 at 5% compounded monthly for 3 years: $10,000 × (1 + 0.05/12)^(12×3) = $11,614.72
APR vs APY: Which Should You Compare?
| Metric | Includes Compounding? | Use When |
|---|---|---|
| APR (Annual Percentage Rate) | No | Comparing loans |
| APY (Annual Percentage Yield) | Yes | Comparing savings/investments |
A credit card advertising "18% APR" with daily compounding actually costs you an effective 19.72% APY. For savings accounts, a "5.00% APY" is what you actually earn — it already includes compounding.
How Compounding Frequency Matters
The same stated rate produces different actual returns depending on how often interest compounds:
| Frequency | 5% APR → APY | Extra on $10K/yr |
|---|---|---|
| Annually (1×) | 5.000% | $0 (baseline) |
| Quarterly (4×) | 5.095% | $9.50 |
| Monthly (12×) | 5.116% | $11.60 |
| Daily (365×) | 5.127% | $12.70 |
The Rule of 72
A quick shortcut: divide 72 by your interest rate to estimate how many years it takes to double your money. At 6% interest: 72 ÷ 6 = 12 years to double. At 8%: 72 ÷ 8 = 9 years.
Convert between APR and APY and see the impact of compounding
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