Actually, the killer gains 100% of the gold and the assist gold of 62.5% is divided between the assisters. This has some weird properties. For example, if you grab first blood, the assister ALSO gains 100 gold in addition to the natural amount of assist gold.
If you have 5 people, and someone kills the person worth 500 gold, then the amount of gold that flows into the system is 500 + 312.5, with roughly 80 gold per assist. On the other hand, if there is only 1 assist, they get the full 312.5 gold.
That last part details why bot lane can snownball quickly; each death gives 162.5% gold to the enemy team of what it would give in a normal lane.