Austin needs to purchase a new heating cooling system for his home. He is thinking about having a geothermal system installed but he wants to know how long it will take to recoup the additional cost of the system. The geothermal system will cost $20,000. A conventional system will cost $7,000. Austin is eligible for a 30% tax credit to be applied immediately to the purchase He estimates that he will save $1,500 per year in utility bills with the geothermal system. These cost of capital (or interest rate) for Austin is 7%. How long will Austin have to use the system to justify the additional expense over the conventional model? (i.e, What is the DISCOUNTED payback period in years?. Also at the interest rate of 8% what is the NPV of this project?