Vital Silence Corporation has just issued a $30-$year callable, convertible bond with a coupon rate of $6\mathrm{.}9$ percent and annual coupon payments. The bond has a conversion price of $$94\mathrm{.}70.$ The company's stock is selling for $$26\mathrm{.}10$ per share. The owner of the bond will be forced to convert if the bond's conversion value is ever greater than or equal to $$1,190.$ The required return on an otherwise identical nonconvertible bond is $7\mathrm{.}7$ percent. Assume a par value of $$1,000.$

a$.$

What is the minimum value of the bond? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ If the stock price were to grow by $11\mathrm{.}1$ percent per year forever, how long would it take for the bond's conversion value to exceed $$1,190?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$