TFT-Gold: was Ausgeben jetzt wirklich kostet

Because the gold you hand over was also earning you interest. Spending drops you onto a lower rung, so from that turn on you collect less every turn, and the shortfall piles up on top of the price you already paid.

With thirty gold, five income a turn, one interest per ten held and a cap of five, spending ten leaves you fourteen behind five turns later. Four of that was never quoted as a price.

Yes, and the boundary is exact rather than a feeling. Once you are holding more than interest can ever pay for, the gold sitting there earns you nothing by sitting there, so spending it costs its price and nothing else.

In the ladder below that is the point where the last column reaches zero. Above that line the purchase is genuinely free; below it, it never is.

Because interest is paid in whole steps, not in proportion to what you hold. What decides the damage is which side of a step you land on after paying, so holding more can make the very same purchase cost more.

In the table above, twenty gold is the worst place to spend ten, worse than ten and worse than thirty. No rule of thumb produces that, which is the reason the page computes it with your own numbers.

No. The gap widens for a few turns and then freezes, because once both paths are earning the same interest again they gain the same amount every turn. From there you are behind by a fixed amount and no longer falling further.

What the page cannot judge is whether what you bought wins before that gap matters. It prices the delay exactly and leaves the decision where it belongs.