You are a hyperbolic discounter. In fact your discount rate between year \(t\) and year \(t+1\) is given by \(0.05 /(1+t)\) for \(t=0\) (today), 1 (next year), \(2,3, \ldots\). This means the discount rate between today and a year from now is 0.05 . The discount rate between a year from now and two years from now is 0.025 . And so forth.

You are considering an investment in energy conservation (better insulation for your house) that has a lifetime of 5 years. It will cost you \(\$ 130\) to install and will reap benefits in terms of energy saved of \(\$ 10\) in year \(1, \$ 20\) in year \(2, \$ 30\) in year \(3, \$ 40\) in year 4 , and \(\$ 50\) in year 5 .

a. Calculate your discount factors for each of the next 5 years.

b. What is the net present value of the energy savings?

c. Is the insulation a good investment for you?

d. Would the insulation be a good investment if your discount rate were a constant \(5 \%\) over the 5 years?