ou are buying a house and will borrow $$197,000$ on a $25-$year fixed rate mortgage with monthly payments to finance the purchase. Your loan officer has offered you a mortgage with an APR of $5\mathrm{.}00\%.$ Alternatively, she tells you that you can $$buy down$$ the interest rate to $4\mathrm{.}75\%$ if you pay points up front on the loan. A point on a loan is $1\%($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$.,32\mathrm{.}164.)$