Compound interest of index funds has nothing to do with the fixed investment of index funds, but because the fund itself is compound interest. Investors don't buy index funds, they don't have to make fixed investment, and the funds are also compound interest. As long as the investment funds are compound interest.

Fund income is reflected in the increase of net value. After the net value increases, the net value change of the next trading day is based on the net value of the previous trading day, so the fund is a compound interest product, just like a stock. Fund income is updated every trading day and compound interest every day.