Very very good job!! You could call it étude in C major.
This was bad for me, because I'm currently doing a set of 24 études (intermediate, maybe early advanced, 4-6 in 8 grade level) and one of the études I was preparing was very similar to this. I was going to take a walking bass and semiquavers "answering" up, but I guess even if the factors are neighbours, the product doesn't have to be equal, (Key was E minor).
If i had to criticise one thing is that the end of C chord with E as as the root note instead of C, doesn't convince to and end, but if you wanted to produce a end that represents that there's something else coming, then it's good. Great job again!