# Banks providing loans

Banks are providing loans.

While granting a loan two scenarios can take place

1. The Loan is repaid
2. The Loan is not-repaid

The benefit from a re-payed loan is small profit. (Let's say 5% in general) The loss from a not re-payed loan is huge loss. (you lost all your investments)

Are there formulas that can calculate the ratio of loss of (based on pseudo-numbers for example) or other theories related to this issue?

If you have an estimate of the probabilities of each scenario, say with probability $$p\in[0,1]$$ the loan is repaid (assuming no other scenario exists), then you can calculate the expected value of making the loan of size $$L$$:
• In scenario 1, payoff is $$-L+(1+0.05)L=0.05L$$ (giving out $$L$$ and getting back the principal plus interest)
• In scenario 2, payoff is $$-L$$ (giving out $$L$$ and getting nothing back)
The expected payoff from making the loan would be $$$$EV=p(0.05)L+(1-p)(-L)=1.05pL-L.$$$$