Solve the following problems:

1. If a machine costs $15,000 to buy and the operating costs are $1,000 at the end the first year, $1,200 at the end of the second, and so on, $200 more per year , until 12 years. What is the present worth of the machine if the nominal interest rate is 15% per annum compounded semi-annually?

2. If the operating costs in the problem above start today instead of the end of the first year, what is the present value at time zero over the 12 years?