A university graduate borrows plo$6000\mathrm{.}00$ to buy a plot. The bank chargs intaest at an annual rate of $9\%$ Assuming that interest is compounded continuously and the borrower makes payment continuously at a constant rate $k,$ determine

$($a$)$ The payment rate $k$ that is required to pay off the loan in four years. b$)$ How mach interest is paid during the four years period?