Question: The capitalized cost of an asset is the sum of the original cost and the net present value of maintaining the asset. Suppose a company is considering the purchase of two different machines. Machine 1 costs $10,000 and t years from now will cost \({{M}_{1}}\left( t \right)=1000\left( 1+0.06t \right)\) dollars to maintain. Machine 2 cost only $8000, but its maintenance is \({{M}_{2}}\left( t \right)=1100\).

(a) If the cost of money is 9% per year compounded continuously, what is the capitalized cost of each machine? Which machine should the company purchase?