$11.$ You are purchasing a new home and need to borrow $$325,000$ from a mortgage lender. The mortgage lender quotes you a rate of $6\mathrm{.}5\%$ APR for a $30-$year fixed rate mortgage $($with payments made at the end of each month$).$ The mortgage lender also tells you that if you are willing to pay $1$ point, they can offer you a lower rate of $6\mathrm{.}25\%$ APR for a $30-$year fixed rate mortgage. One point is equal to $1\%$ of the loan value. So if you take the lower rate and pay the points you will need to borrow an additional $$3250$ to cover the point you are paying the lender.

Required: Assuming that you do not intend to prepay your mortgage $($pay off your mortgage early$),$ are you better off paying the $1$ point and borrowing at $6\mathrm{.}25\%$ APR or just taking out the loan at $6\mathrm{.}5\%$ without any points?