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Indentured servitude took several forms in the colonial period. A web site here discusses this.
Indentured servants were men and women who willingly signed a contract in which they agreed to work for a certain number of years to compensate for their voyage to America.
Three different types of indentured servant agreements existed in the 18th century: free-willers, Kingβs passengers, and redemptioners.
The third category, the redemptioners, seems to best fit the focus of the question, and indeed mentions a timeline to repay the voyage costs before having their contract sold on the open market:
Free-will indentured servants decided to come to America on their own merit and willingly signed a contract before departing England. Kingβs passengers, also known as convict servants, were criminals who were sent to America to serve a term of seven or fourteen years, depending on the crime they committed. Finally, redemptioners were passengers who were given two weeks to redeem the price of their voyage once they got to America and if they were unable to make the payment, they were sold to the highest bidder.