$1.$ A diesel generator for electrical power can be purchased by a remote community for $$350,000$ and used for ten years, when its residual value will be $$50,000.$ Alternatively, it can be leased for $$42,500$ per year, with payments at the start of each year. The community$$s interest rate is $9\%.$

$($a$)$ What is the interest rate for leasing vs$.$ buying? Which is the better choice?

$($b$)$ The community will spend $$80,000$ less each year for fuel and maintenance, than it currently spends on buying power. Should it obtain the generator? What is the rate of return for the generator using the best financing plan?

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