A loan is to be repaid with semi$-$annual payments of $$2000$ over $8$ years, first payment due in $6$ months. The interest rate on the loan is j$2=10\%$ for the first $3$ years and j$2=6\%$ thereafter. What is the amount of the loan? $($answer to nearest dollar$)$

a

$$21,676$

b

$$22,882$

c

$$24,439$

d

$$27,212$