The issue of payment is clearer in 53:3

     For nothing you were sold,
         without money you shall be redeemed.

My reading is that it is a future event, even though described in the past tense. The prophet (whether one thinks of the historical Isaiah writing more than a century previously or [Second Isaiah](https://divinity.yale.edu/second-isaiah-chs-40-54-0) writing as the Exile was ending), calls Israel to rejoice because of her coming liberation from captivity. 

How was the redemption achieved: here the prophet portrays it as God's free gift. Elsewhere, the he describes it in terms of Israel enduring punishment for a certain period to pay for her sin, after which God will forgive. This expressed poignantly in Is. 54:
    
    6 The Lord calls you back,
        like a wife forsaken and grieved in spirit,
    A wife married in youth and then cast off,
        says your God.
    7 For a brief moment I abandoned you,
        but with great tenderness I will take you back.
    8 In an outburst of wrath, for a moment
        I hid my face from you;
    But with enduring love I take pity on you,
        says the Lord, your redeemer.

**Conclusion: What has been redeemed? Israel, especially Jerusalem, from Babylonian captivity.  How was this redemption achieved? By God's grace, after a period of suffering and repentance. Although the prophet describes this in the past tense, he is referring to a occurrence in the future, when the Jews returned to Jerusalem.**