You plan to open an annuity on the day you retire. Assume that the annuity will earn interest at a continuous rate of 5%, and that you will withdraw $50,000 per year. A) Write a differential equation satisfied by P(t), the balance of your annuity t years after you retire. B) Find the solution to the differential equation satisfying P(0) = P. C) What is the minimum principal Po such that the annuity will last for 25 years after you retire (with this interest rate and withdrawal plan)? You do not need to simplify your answer, and there is no need to use a calculator to provide an approximate answer. You plan to open an annuity on the day you retire. Assume that the annuity will earn interest at a continuous rate of 5%, and that you will withdraw $50,000 per year. A) Write a differential equation satisfied by P(t), the balance of your annuity t years after you retire. B) Find the solution to the differential equation satisfying P(0) = P. C) What is the minimum principal Po such that the annuity will last for 25 years after you retire (with this interest rate and withdrawal plan)? You do not need to simplify your answer, and there is no need to use a calculator to provide an approximate