E$13-5$ New Wave Pool Corporation is authorized to issue common and $$3$ convertible preferred shares. Each preferred share is convertible into four common shares. On July $2,$ the company issued $100000$ preferred shares for $$110$ per share. The common shares were trading at $$25$ on September $7,$ $$27\mathrm{.}50$ on September $19,$ and $$29$ on September $28.$

Instructions:

On which date or dates would the preferred shareholders consider converting their shares to common? Why?

Journalize the conversion of the preferred shares using the date chosen in part $($a$)$

Assume also that the preferred shares are redeemable at $$115$ per share at the option of the company. How, if at all, will this affect the preferred shareholders$$ decision to convert?