$($Related to Checkpoint $6\mathrm{.}1)($Calculating annuity payments$)$ On December $31,$ Beth Klemkosky bought a boat for $$70,000.$ She paid $$10,000$ down and agreed to pay the balance in $9$ equal annual installments that include both principal and $12$ percent interest on the declining balance. How big will the annual payments be$?$

a$.$ On December $31,$ Beth Klemkosky bought a boat for $$70,000$ and paid $$10,000$ down, how much does she need to borrow to purchase the boat?

$ $($Round to the nearest dollar.$)$