a$)$ On ${18}^{th}$ March $2022,$ Mary took a personal loan of RM$10,000$ from a bank that charged a simple interest rate of $5\mathrm{.}8\%.$ Find the amount paid on ${15}^{th}$ August $2022$ by using Banker's Rule.

b$)t$ years ago, Mary invested $RM30,000$ in a fund that paid interest of $4\mathrm{.}6\%$ compounded semi$-$annually. Find $t$ if the amount of total investment today is RM$43,165.$