Comparison of alternative investments using capitalized costs. A reactor, which will contain corrosive liquids, has been designed. If the reactor is made of mild steel, the initial installed cost will be $$5000,$ and the useful$-$life period will be $3$ years. Since stainless steel is highly resistant to the corrosive action of the liquids, stainless steel, as the material of construction, has been proposed as an alternative to mild steel. The stainless$-$steel reactor would have an initial installed cost of $$15,000.$ The scrap value at the end of the useful life would be zero for either type of reactor, and both could be replaced at a cost equal to the original price. On the basis of equal capitalized costs for both types of reactors, what should be the useful$-$life period for the stainless$-$steel reactor if money is worth $6$ percent compounded annually?