$1.$ Design an appropriate financing program for a farm to purchase an $$60,000$ tractor and related equipment. The machine will be used for $8$ years $($assume salvage value is zero after the $8$th year$).$ The lender requires $5\%$ interest rate and the farmer is to make a $25\%$ down payment. Tell me which type of loan you will choose and why.

a$.$ Calculate the annual payment and the total interest payment.

b$.$ Calculate the annual payment and total interest payment if the lender provides the loan for only $5$ years.

c$.$ Explain why you prefer the loan for $8$ years instead of $5$ years.