Answer:
I believe the APY would be $520 for the rounded version and $520.20 for the not rounded
(not completely certain since i didnt fully understand)
Explanation:
using the formula for calculating compounding semi annualy
A = P(1 + r)t
A= 500(1+0.02)2 (i put 2 instead of one year because its semi annually so twice)
A= 500(1.02)2
A= 500x1.04=$520(rounded)
A=500x1.0404= $520.20(not rounded)
Please correct me if I understood your question wrong