You have a balance of $$22,800$ on your current credit card. The interest rate charged by this credit card is $19\mathrm{.}8$ percent compounded monthly. You plan to make monthly payment of $$450.$ You just got an offer from another credit card to transfer your entire balance to the new card. The new credit card charges interest rate of $4\mathrm{.}8$ percent compounded monthly. By how many months will you shorten the length of time it will take you to pay off your balance if you transfer your balance to the new credit card and maintain; the same planned monthly payment of $$450?$

$42$ months

$50$ months

$46$ months

$54$ months

$58$ months