Question

A bank issues a $150 loan to a borrower, who will repay the loan with probability 0.78, and default and pay $0 otherwise. In this case, the most competitive interest rate the bank can afford to offer is

answer choices

25.5%

26.5%

28.2%

29.9%

Answer 1

The rate of interest should be enough so that bank gets back the same amount of loan it advances. This implies

150 = 150 x (1 + rate of interest) x 0.78 + 0 x (1 + rate of interest) x (1-0.78)

150 = 150 x (1 + rate of interest) x 0.78

150/ (150*0.78) = 1 + rate of interest

1.282 = 1+ rate of interest

rate of interest = 1.282 - 1 = 0.282 = 28.2%.

Hence, Finally answer = 28.2%

**Please hit like if satisfied from the answer**