Under risk neutrality, a factory can be worth $$500,000$ or $$1,000,000$ in $2$ years, depending on product demand, each with equal probability. The appropriate cost of capital is $6\%$ per year. The factory can be financed with proceeds of $$500,000$ from loans today.

$8$a$.5$ pts$.$ Calculate the loan annual promised rate of return $($Show all your work$).$

$8$b$.5$ pts$.$ Calculate the value of the levered equity $($Show all your work$).$

$8$c$.5$ pts$.$ Calculate the expected annual rate of return for the levered equity shareholders $($Show all your work$)$