You are buying a house and will borrow $$185,000$ 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 $4\mathrm{.}20$ percent. Alternatively, she tells you that you can "buy down" the

interest rate to $3\mathrm{.}90$ 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?

Note: Do not round intermediate calculations and round your answer to $3$ decimal places, e$.$g$.,32\mathrm{.}164.$

Answer is complete but not entirely correct.