Question $2(20$ points$)$

A loan of $100,000$ is being repaid by $15$ equal annual installments made at the end of each year at $6\%$ interest annually.

$($i$)$ Find the amount of each annual installment.

$($ii$)$ Find how much interest to be paid in the fifth year.

$($iii$)$ Find how debt is repaid in the fifth payment.

$($iv$)$ Find the balance in the loan immediately after the fifth payment.