Most savings banks advertise that they compound interest continuously, meaning that the amount S(t) in an account satisfies the differential equation dS/dt=rS, where r is the annual interest rate and t is time measured in years.

1. a) Show that an annual interest rate of 8% compounded continuously is the same as an annual interest rate of 8.33% compounded in years.
2. b) Show that an annual interest rate of r compounded continuously is the same as an annual interest rate of e^r-1 compounded annually.