You need to borrow $ $250,000$ to purchase a new house. The bank will loan you the money at an APR of $4\mathrm{.}8\%($monthly compounding$)$ and a $15$ year term $($i$.$e$.180$ monthly payments in total$).$ After making exactly $20$ payments, what is the total amount of interest you will have paid $($rounded to the nearest dollar$)?$ The total amount of interest is closest to: