Why does Prospero reward Ferdinand in The Tempest?

In addition to the suspicion many fathers feel concerning the general unworthiness of any men aspiring to marry their daughters, Prospero is prejudiced against Ferdinand because Ferdinand is the son of King Alonso and Alonso had helped Antonio usurp Prospero’s dukedom. Despite this prejudice, Prospero also is scheming to have the two marry for dynastic reasons.

In Act III of The Tempest, Prospero decides to test Ferdinand's love and ability to endure hardship for the sake of love. He has Ferdinand do the work of Caliban, carrying and stacking logs. While Ferdinand is at his labors, Miranda appears and they talk. Miranda offers to help Ferdinand but Ferdinand refuses and demonstrates his love for Miranda and sense of duty and responsibility. Prospero, overhearing their conversation, realizes that Ferdinand in genuinely in love with Miranda and will make a good husband for her. Prospero explains “All thy vexations/ Were but my trials of thy love, and thou/ Has strangely stood the test” (Act IV, Scene 1, lines 5-7). Moreover, Prospero understands that having Ferdinand marry Miranda will be a good way to end his feud with Alonso and return to his Dukedom. Thus he rewards Ferdinand by giving him permission to marry Miranda.

How does Prospero compensate Ferdinand for his hard labor in The Tempest?

Prospero doesn't want Ferdinand to win Miranda's hand in marriage too easily; Prospero fears that, if Ferdinand does so, he won't properly value his daughter. Therefore, Prospero sets Ferdinand to hard labor in order to test his worthiness as a prospective husband to his beloved daughter.

One of these tasks is the work of carrying logs. This is a job that, while hard, Ferdinand does willingly. Usually this is Caliban's chore. Prospero spies on Ferdinand as he is going about this task. He witnesses Ferdinand and Miranda talking. Miranda wants to help him with his job, but Ferdinand won't hear of it.

Prospero is pleased with what he overhears because it means Ferdinand is a hard-working and fit husband for his daughter. He plans to reward Ferdinand for this hard work by giving him Miranda's hand in marriage.