Compound interest and exponential functions

Use the sliders to change the annual interest rate (APR) and the number of times per year interest is compounded. Notice that the red graph is how interest works: there is no change until the end of the period, then interest is computed and added. The green graph, h(x), is the exponential function that grows at the interest rate per year, but it grows continuously. The purple graph, k(x), shows continuous compounding: if interest is added every instant. This is the most you can get by shortening the compounding period.