A conglomerate corporation$$ develops, manufactures, and markets a wide range of$$ products, including medical diagnostic imaging$$ devices, jet$$ engines, lighting$$ products, and chemicals. In$2013,$ the stock price rose $34\mathrm{.}08\%,$ and in$2014,$ the stock price declined $8\mathrm{.}6\%.$ If one purchased$$ $$1,000$ of some social media stock at the start of$2013,$ its value would be $$$$2$ comma $935\mathrm{.}64$ at the end of $2014.$ Complete parts$($a$)$ through$($c$)$ below.

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Part $1$

a$.$ Compute the geometric mean rate of return per year of the$$ two$-$year period $2013$dash$2014.($Hint: Denote an increase of $34\mathrm{.}08\%$ as Upper R $1$equals$0\mathrm{.}3408).$

The geometric mean rate of return is

$$

enter your response here$\%$ per year.

$($Round to two decimal places as$$ needed.$)$