Linear vs. Exponential Growth

Property Simple interest grows linearly because it adds the same amount each year. Compound interest grows exponentially because it pays interest on the previously earned interest as well as the principal. Explanation Picture a race between a turtle (simple interest) and a rabbit (compound interest). The turtle plods along at a constant, steady pace. The rabbit starts slow but gets faster and faster, covering more ground with each hop. While the turtle makes progress, the rabbit will eventually be miles ahead! That's why compound interest builds wealth so much more powerfully. Examples After 10 years, 5000 dollars at $6\%$ simple interest becomes $5000 + (5000 \cdot 0.06 \cdot 10) = 8000$ dollars. After 10 years, 5000 dollars at $6\%$ compounded annually becomes $5000(1.06)^{10} \approx 8954.24$ dollars. The difference is small at first, but after 30 years, simple interest yields 14000 dollars while compound interest yields approximately 28717.46 dollars!