Erica set up a savings fund for his son's education so that he would be able to withdraw $$1,650$ at the beginning of every month for the next $4$ years. The fund earns $3\mathrm{.}90\%$ compounded quarterly.

a$.$ What amount should he deposit today to allow for the $$1,650$ periodic withdrawals? b$.$ How much interest would he earn in this investment?