Many banks advertise that they compound interest continuously, meaning that the amount of money A (t) in an account satisfies the DE A' = r A, where r is the annual interest rate and t is time in years.
(a) Show that an interest rate of8% compounded continuously gives an effective annual interest rate of 8.329%; that is, the yield is the same at 8% compounded continuously as at 8.329% compounded annually.
(b) Show that an interest rate of r, compounded continuously, gives an effective annual interest rate of er - 1.
(c) Compare the effective annual interest rates for 8 % compounded continuously and 8% compounded daily.