Sometimes interest is payable more frequently. A fixed deposit investment may pay interest quarterly, and car loans and mortgages are paid monthly. This number is denoted by e . It plays a very important role in calculus. An alternative method of deriving the formula for continuously compounded interest is to set up and solve a differential equation .
Similar equations arise in physics, notably in radioactive decay.
This is not a chance occurrence, as there are a number of problems in financial mathematics where the underlying mathematics also models a physical process. Brownian motion describes molecular motion in a fluid, and also the random movements of the stock market. The famous Black-Scholes equation used in options and derivatives pricing has close analogies in equations describing diffusion processes in physics. This can make a significant difference. A 360-day interest year is used in several European countries and the United States.