Problem $6-69$ Calculating Interest Rates $($LO$2)$

You are buying a house and will borrow $$210,000$ 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 $4\mathrm{.}40\%.$ Alternatively, she tells you that you can "buy down" the interest rate to $4\mathrm{.}15\%$ if you pay points up front on the loan. A point on a loan is $1\%($one percentage point$)$ of the loan value. You believe that you will live in the house for only nine years before selling the house and buying another house. This means that in nine years, you w pay off the remaining balance of the original mortgage. What is the maximum number of points that you would be willing to pay now? $($Do not round intermediate calculations. Round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

Maximum points