Problem 1 (20 points) (a) (10 points) Suppose that you invest Do today in an account that gives you a nominal interest rate of r> 0 (e.g. if r = 0.10 then the nominal rate is 10%) per year compounded k times per year. Derive a formula that will give you the time t it takes for your investment to increase to Doro where to > 1. Note: this formula for 7 MUST be in terms of co i.e. you cannot assume any particular value for it. (b) (5 points) Now use the formula that you derived in (a) to find how long it will take to double an investment of $1000 under a nominal interest rate of 6% compounded daily (assume 365 days in a year). (c) (5 points) Compare your time from (b) with the time it takes for the investment of $1000 to double using only simple interest (i.e. NO compounding) at 6% per year interest