1. How many years, roughly, will it take for your money to double at an annual interest rate of a) 2% b) 6% c) 9% d) 15%? e) What is the product of the interest rate in percent and the time required to double your money in years for parts a) through d)? f) The answer to part e) is known as the Rule of 72. Derive the Rule of 72 algebraically by expanding ln(1 + i) in a power series and making whatever other assumptions that you deem necessary. -- It will be helpful to draw a cash flow diagram, or other relevant figure, to guide my thinking. For questions that ask for an answer involving words please respond in complete and concise sentences. Please state explicitly any assumptions that you think you need to solve a problem. Unless specified otherwise, all interest rates in this problem are compound interest rates.