You are buying a house and will borrow $$325,000$ 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 $4\mathrm{.}10$ 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$.,32\mathrm{.}161.)$