Hanna took a $$89,000$ loan at $2\mathrm{.}34\%$ compounded monthly and decided to make end of month payments of $$2,414.$

$1)$ How many payments will Hanna have to make to amortize this loan?

$($rounded to the next higher whole number$)$

$2)$ What will the size of her final payment be$?$

$ $($enter a positive value$)$