Sean contributed equal deposits at the end of every month for $2$ years into an investment fund. He then decided to stop making payments and left the money in the fund to grow for another $4$ years. The fund was earning $3\mathrm{.}23\%$ compounded monthly for the entire period and the accumulated amount at the end of the term was $$120,000.$

a$.$ Calculate the amount in the fund at the end of $2$ years.

Round to the nearest cent

b$.$ Calculate the size of the periodic deposits into the fund.