(3) Suppose that, after the first year, the perpetuity payment decreases by 2% every year. That is, after purchasing the perpetuity, you receive $1,000 at the end of the first send, $980 at the end of the second year, and so on. Suppose the initial cost for this varying perpetuity is also $10,000. (10% annual discount rate) (i) (1pt) What is the present value of this varying perpetuity? (ii) (2pt) Should you invest in this varying perpetuity according to the NPV rule, why or why not? (iii) (2pt) Should you invest in this varying perpetuity according to the profitability index rule, why or why not? (iv) (2pt) Should you invest in this varying perpetuity according to the discounted payback period rule, why or why not? (v) (3pt) Is there a unique IRR for investing in this varying perpetuity and why? If so, is it higher or lower than 10%