Compound interest formula:

x*(1 + (0.08/4)^2 ---- because the interest compounds quarterly, we divide the percent by 8, and since the time is 6 months, it will compound two times (1 quarter = 3 months)

x*(1 + (0.08/4)^2 = x+100 (we need to earn $100 profit)

(1 + (0.08/4)^2 = (x+100)/x

(1 + (0.02)^2 = 1 + 100/x

1.0404 = 1 + 100/x

0.0404 = 100/x

x = approximately 2 475

The closest answer is D.