On August $1,$ you borrow $$180,000$ to buy a house. The mortgage rate is $7\mathrm{.}0$ percent. The loan is to be repaid in equal monthly payments over $15$ years. The first payment is due on September $1.$ How much of the tenth payment applies to the principle balance? $($Assume that each month is equal to $1/12$ of a year.$)$

Group of answer choices

$$615\mathrm{.}32$

$$598\mathrm{.}41$

$$566\mathrm{.}24$

$$543\mathrm{.}22$

$$589\mathrm{.}28$