In the case study for cost analysis explained in the lecture, for the payback period calculation, there are two ways. The difference between the two ways is whether considering the energy savings into the additional expenses in construction. You can use either the gold-certified or platinum-certified case, explain which payback period calculation method you think makes more sense and why.

Engineers determined that a small amount of newly available chemical additives would increase the resistance of a building material by 20%. The factory manager arranged the purchase of the additive through a 5-year contract at a price of $7,000 annually, with an interest of 15% to be installed annually, and an inflation of 10%, starting from one year from now. The annual price is expected to increase by $50 annually starting from the sixth year and thereafter until the year 13. In addition, an initial investment of $3,000 has been made to prepare a suitable site for the contractor to deliver the additive. Find the equivalent total present value of all these cash flows.

Find the question,I hope to write the solution method in detail and write the laws used (EV, PV,..), thanx.