That formula assumes intermediate values can be non-integers. However, the OP wants to buy more shares with each years profit. And shares can only be bought as units. For instance, had the starting number of stock been 10 shares, it would have never increased, as the paid out yearly dividend would not have been enough to buy a new share.

For the OPs values, a starting value of 1000, an interest of 6.78% and 20 years, your formula results in 3714 (rounded to nearest integer). But if you can only buy shares in units, you end up with 3696 shares. Close, but still 0.5% difference.

In reply to Re^2: dividend with recursive routine by JavaFan
in thread dividend with recursive routine by derpp

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