A customer has approached a local credit union for a $20,000 1-year loan at a 10

Question

A customer has approached a local credit union for a $20,000 1-year loan at a 10% interest rate. If the credit union does not approve the loan application, the $20,000 will be invested in bonds that earn a 6% annual return. Without additional information, the credit union believes that there is a 5% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the credit union will lose the $20,000. What is the credit union expected profit?

Explanation / Answer

The probable profit from customer , if he does not default = 20000 * 10 % = 2000

The total expected profit if loan is given = Probablity he defaults * Amount lost + Probability he does not default * amount earned

= 0.05 * -20000 + 0.95 * 2000 = -1000 + 1900 = 900

His total expected profit from lending out = 900

If the money is invested in bonds

Return = 20000 * 6% * 1 year = 1200

Therefore, the union should opt for investing in 6 % bonds.

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