4. An individual with no initial capital invests k dollars per year at an annual interest rate of return 1'. Assume investments are made continuously and interest is compounded continuously. (a) Determine the sum accumulated S (t) at any time t. (b) If r = 3% determine k so that $1,000,000 will be available for retirement in 40 years. (c) If k =$10,000 per year approximate r such that $1,000,000 will be available for retirement in 40 years. This will require solving a nonlinear equation. You can use Newton's method or a software package you have access to