The only contemporary record of the so-called Manhattan Purchase are the following lines from a letter written by Peter Schagen of the Dutch West Indies Company to Dutch government and received on 7 November, 1626: “They have purchased the Island Manhattes from the Indians for the value of 60 guilders. It is 11,000 morgens in size.” Everything else is a story or an attempt at reconstruction.
I saw examples of such attempts in the memorial near the entrance to Battery Park from Broadway, photos of which you see above. Dutch is close enough to German and English that one can puzzle out the meaning of the text (or you can type it into Google translate). The date mentioned for the purchase requires no translation. However, this is speculation, since there is no contemporary record of the date on which the sale was made. I made a quick attempt to fact check the image on the monument, and the clothes shown seem to be accurate enough to be of the period. The coat of arms with beavers and barrels is an anachronism, since this was used by the city of New York much after the purchase.
The area was inhabited by the American people who called themselves Lenni Lenape (and were called Delaware Indians later by settlers). I was intrigued by what the tribe would do with 60 Guilders. They could only use the money to buy things from the Dutch. So eventually the trade must have been goods for land. The later purchase of Staten Island for the same amount of money records that this was the value of tools given in exchange for land. Perhaps it was the same for Manhattan.
There have been learned papers about land-use customs and laws among the Lenni Lenape, and their notions of trade. These constrain our imagination, but it is hard from a layman’s perspective today to understand the calculation which would have resulted in land sales of this kind. Perhaps this is a subject waiting for its definitive popular history book.