These verses were revealed just before the battle of Uhud, which occurred in the year 625 AD (Sayyid Abul Ala Maududi). 
61:11 [It is that] you believe in Allah and His Messenger and strive in the cause of Allah with your wealth and your lives. That is best for you, if you should know.
61:13 And [you will obtain] another [favor] that you love – victory from Allah and an imminent conquest; and give good tidings to the believers.
61:11 – The Muslims, 1400 years ago are told that if they want to achieve eternal Bliss, that they have to believe in God and His Messenger and then strive with their wealth and their lives in HIS cause.
61:13 – The victory of the Muslims over the enemies, 1400 years, did indeed come to place. Islam won the hearts of nearly whole of Arabia by the time Prophet Muhammed (p) passed away. This was done through preaching and hearing the beautiful Message of the Quran.
Dr. Muhammad Asad:
“11 Cf. 9:111 – “God has bought of the believers their lives and their possessions, promising them paradise in return” – which explains the metaphor of a “bargain” (tijarah). My interpolation, between brackets, of the phrase “in this world and in the life to come” is justified by the subsequent verses 12 and 13, one of which relates to the hereafter, and the other to this world.
12 For this rendering of ‘adn, see note 45 on 38:50.
13 Some of the commentators see in this promise of victory a prediction of actual, warlike conquests by the Muslims. It is, however, much more probable that it relates to a spiritual victory of the Qur’anic message, and its spread among people who had not previously understood it.” 
Maulana Muhammad Ali:
“9a. Verses 8 and 9 contain two different prophecies. In the first of these we are told that all attempts to annihilate Islam will fail, and they did fail. In the second it is affirmed that Islam will be made the predominant religion, the truth of which was witnessed by Arabia in the lifetime of the Holy Prophet. But both prophecies have a wider significance. Attempts are still being made to annihilate Islam, and the Divine promise is that all these attempts shall be brought to naught; while the predominance of Islam over all the religions of the world would in time be established, as clearly as it was in Arabia. The commentators say that this predominance will be brought about through the Promised Messiah (Rz). Polytheists, it should be noted, include the Christians, for they adopted the polytheistic doctrine of Trinity.
13a. The prophecy in the previous verse relates to the Hereafter, while that in this verse relates to the victories of the Muslims over the disbelievers.” 
Scholar Abdullah Yusuf Ali:
“5444 It would indeed be a great and wonderful bargain to give so little and get so much, if we only knew and understood the comparative value of things-die sacrifice of our fleeting advantages for forgiveness, the love of Allah, and eternal bliss.
5445 The supreme Achievement has already been mentioned, viz: the Gardens of Eternity in the Presence of Allah. But lest that seem too remote or abstract for the understanding of men not spiritually advanced, another type or symbol or metaphor is mentioned which the men who first heard this Message could at once understand and appreciate which ye do love’: Viz.: Help and Victory. For all striving in a righteous Cause we get Allah’s help: and however much the odds against us may be, we are sure of victory with Allah’s help. But all life is a striving or struggle the spiritual life even more than any other: and the final victory there is the same as the Garden of Eternity.” 
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 Sayyid Abul Ala Mawdudi:
“It could not be known from any reliable tradition, but a study of its subject-matter shows that this Surah probably was sent down in the period closely following the Battle of Uhud, for by reading between the lines perceives a clear description of the conditions that prevailed in that period.” (Sayyid Abul Ala Maududi – Tafhim al-Qur’an – The Meaning of the Qur’an – Online source)
 The Message of The Quran translated and explained by Muhammad Asad, page 1170 – 1171
Click to access The_Message_of_The_Quran__by_Muhammad_Asad.pdf
 The Holy Quran Arabic Text with English Translation, Commentary and comprehensive Introduction by Maulana Muhammad Ali, page 1189
 The Meaning Of the Glorious Qur’an: Text, Translation, and Commentary by Abdullah Yusuf Ali, page 400 – 401
Click to access quran-yusuf-ali.pdf