A large water utility is planning to upgrade its SCADA system for controlling well pumps, booster pumps, and disinfection equipment so that everything can be centrally controlled. Phase I will reduce labor and travel costs by $28,000 per year. Phase II will reduce costs by an additional $20,000 per year, that is, $48,000. Phase I savings should occur in years 0, 1, 2, and 3 and phase II savings should occur in years 4 through 10. Let i = 8% per year.

(a) Determine the present worth of the upgraded system for years 1 to 10.

(b) The utility General Manager had hoped for a present worth of at least $400,000. Determine the interest rate at which this would be correct.