Question

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% |

Answer #1

**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%**

A bank faces two types of borrowers, type A and B. Both want a
$225 loan. Type A repays the loan 100% of the time and type B only
repays with probability 0.86. The bank doesn't observe type, but
believes fraction z is type A. What does z need to be so that the
bank can afford a pooling interest rate of 5%?

wo-part question. Only answer number 2, please.
1. There are two types of borrowers in the credit market for
motorcycle loans, type X, and type R. They both need a loan for
$37,600, for a Ducati. Type X repays 96% of the time and type R
repays 84% of the time. If the lending bank, Street Bank, has full
information, then the risk premium for X is ____% and for R it is
____%.
2. Consider the credit market in...

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