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We remember very well those things that we care about a lot. We remember the most important things, the things we have done many number of times and the things we love most.

Generally human beings care about money. We also remind ourselves time and again the most important things we have to do in future.  For persons who care about the money, they always make a plan of what they will do with money.  

So a lender makes plans for reinvestment or for some other use, of the money that he should receive. So he remembers the fact that he lent money.

On the other hand, the person who borrows money, puts the money to use. He thinks of his other activities. Because the return of the money does not give him benefit, he does not often think of that fact.  So he is likely to forget that he borrowed some money.