$(3)$ Mr$.$ Bell buys a home for an unspecified amount. He pays a down payment of $$20,000$ and finances the remainder for $15$ years with level end$-$of$-$month payments of $$1,692.$ The annual effective interest rate for the first five years is $4\%,$ and thereafter it is $6\%.$ Mr$.$ Bell sells the house just after making his $100$ th mortgage payment. The selling price is $$258,000.$ How much money will Mr$.$ Bell get at closing? $($Remember$,$ the loan holder is paid first, and then Mr$.$ Bell receives the balance of the inflow from the resale.$)$