You recently purchased a stock that is expected to earn $10$ percent in a booming economy, $3$ percent in a normal economy, and lose $4\mathrm{.}5$ percent in a recessionary economy. The probability of a booming economy is $13$ percent while the probability of a normal economy is $69$ percent. What is your expected rate of return on this stock?

Multiple Choice

$2\mathrm{.}56\%$

$2\mathrm{.}18\%$

$2\mathrm{.}83\%$

$0\mathrm{.}38\%$

$4\mathrm{.}18\%$