Question

You are seeking a bank loan for $12000 and go to Prosper Bank and to Skyline Bank to see which loan has a lower rate. Your plan is to open a restaurant, which is quite risky. Prosper Bank expects that it could recover $10,000 if you defaulted while Skyline thinks it would only recoup $9000. However, Skyline puts your probability of repayment at 97% while Prosper only has it at 96%. Which loan has the lower interest rate? Assume both banks are aiming to earn 6%.

Answer 1

SKYLINE = 6.96%, PROSPER = 6.94%.

Step-by-step explanation:

So, in the question above we are given the following parameters or information or data as;

=> Amount of bank loan been seeked for = $12000.

=> "Prosper Bank expects that it could recover $10,000 if you defaulted while Skyline thinks it would only recoup $9000."

=> " Skyline puts the probability of repayment at 97% while Prosper only has it at 96%."

=>" both banks are aiming to earn 6%."

So, for both banks we will be making use of the formula below:

L × (1 + RER) = POR × L × (1 + IRCr) + (1 - POR) × RCD.

Where L = loan, RER = required earning rate, POR = probability of repayment, IRCr = interest rate charged and RCD = Recovery in case of default.

(A). FOR PROSPER BANK:

12000 × ( 1 + 6%) = 96% × 12000 × (1 + IRCr) + (1 - 96% ) × 10000.

SOLVING FOR IRCr, we have;

interest rate charged = 6.94%.

(B). FOR SKYLINE BANK;

12000 × (1 + 6%) = 97% × 12000 × (1 + IRcr ) + (1 - 97%) × 9000.

IRCr =6.96%.