A corporate customer obtains a $1.5 million loan from a bank. The customer agrees to pay a 6.25% interest rate and agrees to make compensating balances of 4% of the loan amount. These will be held in non-interest-bearing transactions deposits at the bank for one year. The bank charges a 1% loan origination fee on the amount borrowed. Reserve requirements are 10%. What is the expected rate of return to the bank (k) (to the nearest basis point)?

Question

Quizplus · Accepted Answer

We need to calculate the expected rate of return to the bank (k) which takes into account the interest rate, compensating balances, loan origination fee, and reserve requirements. Using the formula (1 + i)(1 - rb) = (1 + k)(1 - f - cb), where i is the interest rate, rb is the reserve requirement, f is the loan origination fee as a decimal, and cb is the compensating balance as a decimal, we can solve for k. 
Plugging in the values, we get (1 + 0.0625)(1 - 0.1 - 0.01 - 0.04) = (1 + k)(1 - 0.01), which simplifies to 0.8715 = 0.99(1 + k). Solving for k, we get k = 0.0752 or 7.52% to the nearest basis point. Therefore, the best choice is B.

A Corporate Customer Obtains a $1