'reciprocate' has the sense of 'to return in kind or degree' and implies a mutual or equivalent exchange or a paying back of what one has received e.g. reciprocate someone's hospitality by inviting them for a visit.
In this sentence, we have someone buying a car in gratitude for a series of favours. It may be in proportion to the sense of gratitude felt, but a new car versus a few favours is too out of proportion to be called 'reciprocating'.
Thank you guys, but I think I found the phrasal verb I was looking for, it's 'to make up', I am not sure if it fits in that context, I looked it up on a web dictionary, it has lots of meanings, but one of them is 'to compensate', which means you are trying to keep things even.
Let me make you up for helping me out today. You have done too much for me, I will make you up as soon as I can.
Careful there. If I was injured in a traffic accident, the insurance company would give me money to compensate me for the injuries I received, pain and suffering. The insurance company is not 'reciprocating'.
Similarly, 'make up for' is not appropriate for your context. make up for: 'serve or act to compensate for something lost, missed, or deficient' : A worker needing to go home early one day may say to his boss: "I'll make up the time tomorrow."
A boyfriend who had to cancel a date might send his girlfriend some flowers the next day, and take his girlfriend out to a very expensive restaurant next time, to 'make up for' having let her down the previous time.
make it up to: 'compensate someone for negligent or unfair treatment'