An obligation can be settled by making a payment of $$2,000$ now and a final payment of $$4,000$ in seven years $($Alternative $1).$ Alternatively, the obligation can be settled by payments of $$600$ at the end of every six months for eight years $($Alternative $2).$ Interest is $9\%$ compounded semi$-$annually.

Compute the present value of each alternative and determine the preferred alternative according to the discounted cash flow criterion?

a$)$ Alternative $1$

b$)$ Alternative $2$