please show working.
A bank faces two types of borrowers, A and B, both who request a $100 loan. A will repay the loan with probability 1 and default otherwise, while B will repay the loan with probability 0.85 and default otherwise. The bank cannot observe type, but knows that fraction 0.74 of borrowers are type A and the rest are type B. What is the competitive pooling interest rate?
9.6% |
6.6% |
4.1% |
3% |
Ans:
Given data:
A will repay the loan with probability = 1
B will repay the loan with probability = 0.85
A and B both request the loan =$100
Bank knows the fraction=0.74
A) Here we have to findout the total repayment probability:
We knopw the formulas of total repayment probability is
Total repayment probability =( fraction* a having the loan with probability)+( B having the loan with probability*(1- fraction value))
Total probability=(0.74*1) + (0.85*(1-0.74)
=(0.74) + (0.85*(0.26))
=(0.74) + (0.221)
=0.961
Total repayment probability is 0.961
B )here we have to finfd out the competetive pooling intereset rate:
We know the formula of interest rate is,
Interest rate =( ( 1/ total repayment probability) -1)*100
=((1/ 0.961)-1)*100
=(1.0405-1)*100
=(0.045)*100
Interest rate=4.5%
From the question, option 'C' is correct because it is nearer to 4.5%
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