Derek and Meagan Jacoby recently graduated from State University, and Derek accepted a job in business consulting while Meagan accepted a job in computer programming. Meagan inherited $$40,000$ from her grandfather, who recently passed away. The couple is debating whether they should buy or rent a home. They located a rental home that meets their needs. The monthly rent is $$2,550.$ They also found a three$-$bedroom home that would cost $$160,000$ to purchase. The Jacobys could use Meagan's inheritance for a down payment on the home. Thus, they would need to borrow $$120,000$ to acquire the home. They have the option of paying two discount points to receive a fixed interest rate of $4\mathrm{.}50$ percent on the loan or paying no points and receiving a fixed interest rate of $5\mathrm{.}75$ percent for a $30-$year fixed loan.Though anything could happen, the couple expects to live in the home for no more than five years before relocating to a different region of the country. Derek and Meagan don't have any school$-$related debt, so they will save the $$40,000$ if they don't purchase a home. Also, consider the following information:The couple's marginal tax rate is $24$ percent.Regardless of whether they buy or rent, the couple will itemize their deductions and have the ability to deduct all of the property taxes from the purchase of a residence.If they buy, the Jacobys would purchase and move into the home on January $1,2023.$If they buy the home, the property taxes for the year are $$3,900.$Disregard loan$-$related fees not mentioned above.If the couple does not buy a home, they will put their money into their taxable annuity account, where they earn $5$ percent annual interest.Assume that all unstated costs are equal between the buy and rent options.Help the Jacobys with their decisions by answering the following questions:Note: Leave no answer blank. Enter zero if applicable.b$.$ What is the approximate break$-$even point in years $($or months$)$ for paying the points to receive a reduced interest rate? $($To simplify this computation, assume the Jacobys will make interest$-$only payments, and ignore the time value of money.$)$Note: Do not round intermediate calculations. Round your final answer to $2$ decimal places.