A stock is expected to pay a dividend of $$1\mathrm{.}0$ one year from now, $$1\mathrm{.}8$ two years from now, and $$2\mathrm{.}3$ three years from now. The growth rate in dividends after that point is expected to be $9\%$ annually. The required return on the stock is $14\%.$ The estimated price per share of the stock six years from now should be $$\_\_\_\_\_\_\_\_\_.$