We have seen that if we invest an amount A at an annual interest rate r compounded n times in a year then after one year we would have A(1+nr)n. What is the approximate rate of change of our money? If we consider the first 1 period of a year in which our money goes from A to A(1+nr) then the change in money is A=A(1+nr)A= while the length of the time period (in years) is t= So the rate of change of money per time is the quotient of these two, which is tA= We conclude that if the time interval is small, then approximately dtdArA This is a familiar differential equation, with solution A(t)=CertA(t)=CertA(t)=eCrtA(t)=Cret