A $5-$year loan in the amount of $$48,000$ is to be repaid in equal annual payments. What is the remaining principal balance after the third payment if the interest rate is $5$ percent, compounded annually?

Group of answer choices

$$22,173\mathrm{.}58$

$$18,294\mathrm{.}24$

$$22,998\mathrm{.}30$

$$18,677\mathrm{.}70$

$$20,614\mathrm{.}89$