Problem $5(10$ Marks$)$ In each of the following independent cases, it is assumed that the corporation has outstanding $20,000,$ $$0\mathrm{.}80,$ preferred shares, with a carrying value of $$200,000,$ and $80,000$ common shares, with a carrying value of $$800,000.$ Although dividends have been paid regularly up to $2020,$ no dividends were declared in $2021$ or $2022.$ a$)$ At December $31,2023,$ the board of directors wants to distribute $$125,000$ in dividends. How much will the preferred shareholders receive if their shares are cumulative and non$-$participating? b$)$ At December $31,2023,$ the board of directors wants to distribute $$200,000$ in dividends. How much will the preferred shareholders receive if their shares are cumulative and participating up to $15\%$ in total? c$)$ On December $31,2023,$ the preferred shareholders received an $$80,000$ dividend on their shares, which are cumulative and fully participating. How much money was distributed in total for dividends?