A sum of money is deposited at the beginning of each year for $3$ years at $12\%$ compounded annually. After the last deposit interest for the account is to be $8\mathrm{.}24\%$ compounded quarterly

and the account is to be paid out by payments of $$370\mathrm{.}00,$ made at the beginning of each quarter for nine years, what is the size of the annual deposit? FULL CALCULATIONS