You are a new employee with the Metro Daily Planet. The Planet offers three different retirement plans. Plan 1 starts the first day of work and puts $1,000 away in your retirement account at the end of every year for forty years. Plan 2 starts after ten years and puts away $2,000 every year for thirty years. Plan 3 starts after twenty years and puts away $4,000 every year for the last twenty years of employment. All three plans guarantee an annual growth rate of 8%. a. Which plan should you choose if you plan to work at the Planet for forty years? b. Which plan should you choose if you plan to work at the Planet for only the next thirty years? c. Which plan should you choose if you plan to work at the Planet for only the next twenty years? d. Which plan should you choose if you plan to work at the Planet for only the next ten years? e. What do the answers in parts (a) through (d) imply about savings?