You are considering purchasing a house for $$875,000.$ You will make a $20\%$ down payment. You have the following $30$ year fixed rate mortgage interest quotes from your bank:Possible Interest rates: $7\mathrm{.}25\%$ interest rate with $0$ points, $7\mathrm{.}00\%$ interest rate with $1\mathrm{.}45$ points, and a $6\mathrm{.}95\%$ interest rate with $2\mathrm{.}35$ points. In addition to any points, in all cases you will have to pay a $1\%$ origination fee to get the loan.

a$)$ If you will pay all fees and points yourself, which of the three is the better deal based on the calculated APR? Show the APRs for all three alternatives and explain why the one you chose is the better deal. Show your work.

b$)$ If you decide to finance the fees and points rather than pay them yourself up front, how much additional interest will you pay over the full life of the loan alternative you chose? Do this one just for the best loan alternative from a$).$