Comment on rb > c

In my opinion, the "equation" - which is not really an equation because it is an equality - makes complete sense. Generally, people would do good only because they want something good in return. This repayment can be made in any form: money, deed, land, toys, anything. This would be very logical and sensical. However, this idea assumes the worst out of humans or animals. It is saying that we would never do good just for the sake of goodness.
I know of someone, an elderly. She lives a simple life, dresses like a normal middle income lady, speaks like a normal middle income lady, and lives like a normal middle class lady. However, she has an extraordinary heart. I have heard many stories of her helping other people. She has given so much money to others. Almost everytime I went to her house she would give me ten dollars.
It is very sad to hear about some people that she had lent money to forgetting about her deeds. Some even ask for more money, with the claim that they need the money to support his family. However, many a times I hear that the person was not supporting his family but instead spent the money on gambling and beers. However, the generous lady still helped this man. She has never asked for her money back. This is strange. She does good but does not expect good. She does good when the cost of doing goodness is more than the deed itself.
Therefore, I disagree with the rb > c. It just does not fit with my principles, and my belief of human nature.