Remember - draw cash flow diagrams where appropriate and put answers in boxes. You may complete on a separate piece of paper- just print legibly and put boxes around your final answer and scan in to submit. SHOW YOUR WORK 1. Arithmetic and Geometric Gradient (DRAW the Cash Flow Diagram) a) The United State Post Office (USPS) unknowingly got trapped into a single-source situation with their new routing system. The vendor now wants USPS to pay software update and maintenance management costs starting at $12,000 a year for the first year and increasing $50 per year for the next 40 years. Consider 6% interest compounded annually. What is the present value of these increasing maintenance costs? b) Engineers at the Grand Ethiopian Renaissance Dam, using asset management tools, have identified that one of the 3 spillways will need to be replaced in 7 years at a cost of $50,000 in that year (year 7). The corporation wants to put aside some amount of money every year starting from year 1 and add $1,000 each year to the amount of money they put aside starting in year 2 instead of putting aside a constant amount of money (arithmetic gradient, not just an annuity). How much should the Dam start putting aside in year 1 to have the money to replace the failing spillway in 7 years with this plan? Assume a 10% interest rate compounded annually.