Katherine wants to accumulate at least $55,000 by depositing $2,200 at the end of every month into a fund that earns interest at 5.75% compounded monthly. (Please solve algebraically)

a) How many deposits does she need to make to reach her goal? (Round to the next payment)

b) How long will it take Katherine to reach her goal? (Express the answer in years and months, rounded to the next payment period)