Suppose that Apple Inc. $($Apple$)$ is selling for $$115\mathrm{.}00.$ Analysts believe that the growth rate for Apple will be $30\%$ per year for the next two years, $20\%$ per year for the following three years, and thereafter the growth rate will be $8\%$ indefinitely. Apple$$s most recent cash dividend per share was $$3\mathrm{.}00.$ The dividend will grow by the same rate as the company. Stockholders require a return of $20$ percent on Apple$$s common stock.

Required:

a$)$ Based on the above assumptions, determine the price of Apple$$s common stock.

b$)$ Explain whether an investor should buy the stock.