入学金 is a good example of unspecified expenditure. Not only you in Japan wonder why and for what they have to pay it. I found this and last post from internet and I think it well explained in English. (it isn't my work but I thought would be nice to put it here for you :)) *I wish I could find something in Mandarin ....

金: A general term for money in specific situations, not necessarily in exchange for something, might even not cost. It's a fallback option when none of the rest could apply. 保証金, 入学金, お祝い金, 所持金, 補助金, 契約金, 敷金, 賠償金 ～料: Charge or fee for activities done, typically charged by organizations with a predetermined amount of money. 授業料, 手数料, 送料, 使用料, サービス料, 通行料, キャンセル料 ～代: Price or charge in exchange for concrete (doesn't mean tangible) items. Most widely used. 食事代, 飲み代, タバコ代, バス代, バイト代, 電気代, 地代, 修理代 ～費: Overall expenses for specific activities, not used for detailed items. 医療費, 交通費, 学費, 生活費, 食費, 参加費

こんにちは、私は日本生まれ、育ちですが、違いを考えたことがありませんでした！ 入学金、入学料、入学代、入学費、正しい使い方だと思います。 ただ、～～～金、は私は避けてつかいます、それはお金という言葉を直接的につかっていて、すこし印象がよくないと感じるからです。（ I usually avoid using 金　because it sounds very direct word )