Commentary for Kiddushin 31:11

A slave may also go free by essentially buying himself back. This is done by dividing the purchase money into the number of years of acquisition. Then the amount the person has worked is reduced, the slave pays back the rest and goes free.

A baraita teaches that a slave goes free either by money, money’s equivalent or a document. The first two are easy to understand and are anchored in the verse. But what about the document? What kind of a document is this? If it is just an IOU, then it is equivalent to money. And seemingly it should not be a document of manumission, because we would think that a slave does not really need a document of manumission. It should be enough that the master simply tells him to go free.
This leads Rava to say that the slave actually belongs bodily to his master and cannot go free without a document of manumission. An oral declaration is not enough.