There were a few things from the conversation that made me decide to proceed. Firstly, Utah would be reducing the tax credit over the coming years so if I wanted to take advantage of those credits, I shouldn't wait. Secondly, I had provided them with my electric usage for several months and he said my usage was really high in comparison to others with my size house. I was intrigued by the idea of offsetting those high costs (assuming it was true) with "free" power from the Sun.
I sat down and did the math with the goal of determining if purchasing a solar assembly on credit would pay for itself. There are actually a lot of unknowns in this equation (the weather being the biggest outlier).
The total cost of the installation was $15,000.00. This is a 3 kilowatt system.
The tax credit is 25% up to a maximum of $2,000.00 per residence. So figure $2,000 since 25% is $3,750.
See https://le.utah.gov/xcode/Title59/Chapter10/59-10-S1014.html
The federal tax credit is 30% (until 2019) with no maximum. So figure $4,500.
See https://energy.gov/savings/residential-renewable-energy-tax-credit
So total credits = $2,000+$4,500=$6,500 making the cost $8,500. I've heard there may be other credits but so far I don't know what they are.
The system has a 25 year manufacture warranty. The loan is 3% for 12 years with a payment of $124 a month. If I apply the credit to the balance, the loan could be paid off in 6-7 years.
So to answer the question, "will the solar array pay for itself", I roughly use the $124 monthly loan amount as the target number. If I save $124 in electricity each month, it is paying for itself...