$($a$)$ You consider buying a stock that is expected to pay a dividend of $$2$ one year from today, and another dividend of $$10$ three years from today. You expect to sell the stock at a price of $$60$ at the end of $4$ years. The required rate of return on equity is $10\%.$ How much would you be willing to pay for the stock today?

$($b$)$ Shares of the Katydid Co$.$ common stock are currently selling for $$27\mathrm{.}73.$ The last dividend paid was $$1\mathrm{.}60$ per share. The market rate of return is $10$ percent. At what rate is the dividend growing?