Question

A commercial banks offers $500 loans and there are two types of borrowers, A & B. Type A repays the loan 95% of the time, and type B repays the loan 79% of the time. Under perfect information, at the competitive interest rates, type A must make a repayment of ____ and type B repays ____.

Group of answer choices

$526.32; $632.91

$526.32; $624.44

$533.45; $632.91

$533.45; $624.44

Answer 1

Suppose bank charges a rate of X% from type A and Y% from type B. Then bank will be receiving 500 + 5X from type A and 500 + 5Y from type B, in case the loan is repaid. The expected amount of loan bank will be receiving from type A is E(A) = 0.95*(500+ 5X) + 0.05*0 which is equivalent to E(A) = 475 + 4.75X. Similarly, the expected amount of loan bank will be receiving from type B is E(B) = 395 + 3.95Y. This should be enough to cover the loan of 500. Hence we have

475 + 4.75X = 500 and 395 + 3.9Y = 500

X = 5.26% and Y = 26.62%

Thus, type A pays 500 + 5*5.26 = 526.32 and type B pays 500 + 5*26.62 = 632.91

Select $526.32; $632.91