You are considering the purchase of a new home. You intend to borrow $$275,000.$ You are discussing financing options with a mortgage broker. The mortgage broker tells you that you may take a $30-$year loan, with monthly payments, at an interest rate of $5\mathrm{.}75\%/$annum$.$ Alternatively, you may take a $15-$year loan, also with monthly payments, at an interest rate of $5\mathrm{.}0\%/$annum$.$ The first payment on either loan will be due one month from the closing date of the loan.

What is the monthly loan payment on the $30-$year loan? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

What is the monthly loan payment on the $15-$year loan? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

What is the Effective Annual Interest Rate of the$-30$ year loan? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Assume that you will live in the house for the entire term of the $30-$year loan and make all payments on time, how much interest would you save by financing the house over $15$ years as compared to financing it over $30$ years?