You are buying a house and will borrow $$275,000$ on a $30-$year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of $4\mathrm{.}10$ percent. Alternatively, she tells you that you can $$buy down$$ the interest rate to $3\mathrm{.}75$ percent if you pay points up front on the loan. A point on a loan is $1$ percent $($one percentage point$)$ of the loan value. How many points, at most, would you be willing to pay to buy down the interest rate? $($Do not round intermediate calculations and round your answer to $3$ decimal places, e$.$g$.,32\mathrm{.}161.)$