Nicole borrows $$278000$ for $10$ years at a nominal rate of $4\mathrm{.}2$ percent convertible monthly. She has the option of paying off the loan using either the amortization or sinking fund method. If the sinking fund has an interest rate of $5\mathrm{.}4$ percent convertible monthly, how much will she save each month by going with the better method? $($Assume monthly payments and deposits.$)($Note: you'll need to decide which method is the better one.$)$

Answer: $