Question

# please show working. A bank faces two types of borrowers, A and B, both who request...

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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