Although Prospero has picked Ferdinand out as a husband for Miranda, he still wants to test whether the young man is worthy of her love. As Ferdinand carries logs—normally Caliban's work—Prospero secretly observes him. Ferdinand does the work willingly, and when Miranda offers to help, he refuses to let her.
Ferdinand expresses his willingness to be a "slave" for Miranda. Prospero looks with approval at the love blossoming between the two. Miranda, who has been isolated all her life, is open about her love, not knowing it might be safer to hide it. However, with Ferdinand, her love is in no danger of being taken advantage of.
Willingness to labor is a sign of love and worth in this novel. Ariel, for example, shows his love for Prospero by willingly working for him. However, unsurprisingly, these characters also want their rewards in the end, be it freedom or the hand of a beloved in marriage.