Compound interest

Property Compound interest is interest that is paid on both the principal and on previously earned interest. The formula is $A = P \left(1 + \frac{r}{n}\right)^{nt}$. Explanation This is where the real magic happens! Think of compound interest as a snowball rolling downhill. It picks up more snow, gets bigger, and then picks up even more snow because it’s bigger. You earn interest on your original principal AND on the interest you've already accumulated. This chain reaction makes your money grow exponentially faster over time! Examples Investing 3000 dollars at $5\%$ compounded annually for 10 years yields $A = 3000(1 + 0.05)^{10} \approx 4886.68$ dollars. The same 3000 dollars at $5\%$ compounded quarterly for 10 years yields $A = 3000(1 + \frac{0.05}{4})^{4 \cdot 10} \approx 4930.86$ dollars. A 1000 dollars credit card purchase at $20\%$ compounded monthly for 1 year becomes $A = 1000(1 + \frac{0.20}{12})^{12 \cdot 1} \approx 1219.39$ dollars owed.