A $10$ year loan of $1,000$ with effective annual rate $10\%$ can be paid off with $10$ annual payments of $K$ each at the end of each year. It can also be paid off by $10$ interest only payments and depositing the would$-$be PR$\text{'}$s into a sinking fund paying $j$ and pay the principal at time $10.$ Find the net balance at time $10,$ where positive balance means that you owe money to the bank.

$($a$)|)|)$

$($b$)|)|)$

$($c$)|)|)$

$($d$)|)$

$($e$)$ none of these