Brian borrows $$10,000$ for $10$ years at an annual effective interest rate of $10\%.$

$($a$)$ Find the level amortization payment $X of this loan.

$($b$)$ Suppose that Brian decided to use a sinking fund instead of the amortization method to pay off

his loan. To do so$,$ he starts a sinking fund that has an annual effective rate of $14\%.$ At the end of

each year, he pays only the interest on the loan and deposits $X minus the interest into the sinking

fund. What is the balance of the sinking fund immediately after Brian pays off the loan?

$($c$)$ Which one of the above two methods of repayment of the loan would you prefer? Why so$?$