$1.$ A company just paid dividends of $$2\mathrm{.}75$ per share. The company has a constant growth of $5\mathrm{.}5\%.$ The risk$-$free rate is $2\mathrm{.}5\%,$ beta is $0\mathrm{.}90$ and market return of $8\%.$ The stock is selling at $$75\mathrm{.}50.$

$1.$ Determine the rate of return on equity.

$2.$ What is the stock price after a year?