A $10-$year loan of $120,000$ is to be repaid with payments at the end of each month. Interest is at an annual effective rate of $6\mathrm{.}00\%.$

The first monthly payment is $800.$ Each additional payment will be $k$ more than the previous month payment. Find $k.$

A $9\mathrm{.}73$

$9\mathrm{.}16$

$9\mathrm{.}60$

$9\mathrm{.}97$

$9\mathrm{.}52$