A person purchased a $$216,717$ home $10$ years ago by paying $15\%$ down and signing a $30-$year mortgage at $11\mathrm{.}4\%$ compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new $20-$year mortgage at $5\mathrm{.}4\%$ compounded monthly. How much interest will refinancing save?

Money Saved: $ $($Round to the nearest cent as needed.$)$