The provincial government's Ministry of Fisheries requires a new patrol boat. The price of a Songster is $45,000, and its annual operating costs will be $5,000. It will be sold for about $10,000 after 4 years, and replaced. A more durable and more efficient Boston Wailer, priced at $66,000, would cost $4,000 per year to operate, last 6 years, and have a resale value of $20,000.

(a) If the provincial government pays an interest rate of 8% compounded annually on its midterm debt, which boat should they choose? [7 marks]

(b) The manufacturer of the boat that you do not choose has offered a manufacturers rebate payable one year after purchase. How large must the rebate be so that the two boats have the same annual cost?