Bunuel help understand if my approach is correct.
Can I use successive change formula ?
X% (change) + Y% (change) = X+ Y + [XY/100]
so in this case x=2, y=3, z=4
2+3+4+ 24/100
->9.24 is the % increased.
there for 9.24% of 10,000 is 924.
in the options the closest value to 924 is 926.24.
so we can go ahead with this option.
Ans 926.24
Bunuel
If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.
Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;
Total: 200+306+(~420)=~$926.
Answer: E.