A small company wishes to set up a fund that can be used for technology purchases over the next $6$ years. Their forecast is for $$22,000$ to be needed at the end of year $1,$ decreasing by $$2,000$ each year thereafter. The fund earns $10\%$ per year. How much money must be deposited to the fund at the end of year $0$ to just deplete the fund after the last withdrawal?

$$76447$

$$67447$

$$64477$

$$46447$