1. Currently, two options are available for modernization of a pumping station in a water treatment facility. Option 1 is to install a pumping system which is more durable at a cost of $20,000. With this option, the system will require to be replaced every 15 years. The maintenance cost for this system runs at $4,000 every five years. Option 2 is to install a cheaper pumping system. It costs $12,000. However, the system must be replaced every 6 years. The maintenance cost for this system is $1,600 every 2 years. Compute the present worth capitalized cost for each option and decide which one would be to our advantage. The interest rate is at 7% per year.

2. For some interest rate i and some number of interest period n, the uniform series capital recovery factor is 0.0854 and the sinking fund factor is 0.0404. Compute the interest rate i.

3. A riverfront walkway was constructed for $1,000,000. The annual maintenance cost is $12,000 per year. It is also estimated that a repair cost of $100,000 will be needed at the time the walkway reaches its half useful life. Using an annual interest rate of 4% and a useful life of 40 years, compute the present worth of this activity.

4. Two alternatives are suggested for improvement to a power generation plant. Alternative A costs $60,000 and provides yearly benefit of $16,000. Alternative B requires $84,000 of initial cost. However, it will yield benefits in the order of $22,000 per year.

(a) For the investment period of 3 years and an interest rate of 6%, use the net present worth method and find out which alternative is better. (b) Repeat Part (a) but use the equivalent uniform annual cost analysis method. (c) Repeat Part (a) and use the rate of return method and n =5 years. (d) Considering Alternative A, take the investment period as an unknown and compute the breakeven period.