The benefits of reading Ramayana are mentioned in the Ramayana itself:
He who listens every day to this oldest epic, composed by the sage Vālmīki, which is calculated to bestow religious merit, renown and longevity, and which lends support to the Vedas, is completely freed of sin. Kings will overcome their enemies and conquer the earth, men will overcome all difficulties and women will be blessed with excellent sons and grandsons. Those listening to this epic will receive from Śrī Rāma all the boons they desire. Through a hearing of this work all the gods are satisfied. One who keeps a copy in his house will find all his obstacles coming to an end. A man offering worship to and reading this historical work is completely rid of all sins and attains a long life; all the gods are thus pleased and one’s ancestors are gratified forever. Those transcribing this work with devotion are guaranteed residence in heaven, while those hearing it will secure the growth of their family and wealth, supreme happiness and the accomplishment of all their objects on earth.
The gods, Gandharvas, Siddhas and ṛṣis always listen with great pleasure to the Rāmayana in heaven. This legend is the bestower of longevity, the enhancer of fortune and the dispeller of sins. It is the equal of the Vedas. A man reading even a quarter of it is freed from all sins; indeed, even if one sins daily he is released from the reactions if he recites just one verse of the Rāmayana. A man gets the results of one thousand Ashvamedha sacrifices and ten thousand Vajpeya sacrifices merely by hearing this great work. He has visited all the holy shrines and bathed in all the sacred rivers. One who listens to the story of Śrī Rāma with full reverence roots out all sins and goes to the world of Viṣṇu. The Rāmayana is the unsurpassed form of Gayatri. By hearing it with devotion one will undoubtedly achieve liberation, along with many generations of ancestors. The exploits of Śrī Rāma are the bestower of all four of life’s objects—dharma, artha, kama and moksha. Hearing even one line of this work with full devotion guarantees one’s attainment of the world of Brahmā.