Elizabeth contributed equal deposits at the end of every month for 5 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 4.05% compounded monthly for the entire period and the accumulated amount at the end of the term was $90,000.

a. Calculate the amount in the fund at the end of 5 years.

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