Of course it is...it's a natural consequence of compound interest. One's ability to accumulate additional wealth scales exponentially with their level of existing wealth.
If you have 3 (or 10) times as much as I have, and we both invest all our money in the same interest bearing account, then after N years you will still have 3 (or 10) times as much as I have.
So, according to your model, the initial wealth distribution should not change. (Of course, you can argue that those with more wealth consume a smaller part of it, and that gives rise to inequality, but that's an issue beyond "compound interest").
EDIT to remove a typo