Question

Consider two loans with​ one-year maturities and identical face​ values: a(n) 8.3 % loan with a 0.96 % loan origination fee and​ a(n) 8.3 % loan with a 5.3 % ​(no-interest) compensating balance requirement. What is the effective annual rate ​(EAR​) associated with each​ loan? Which loan would have the highest Eince the loan origination fee is just another form of interest. C. The loan with the compensating balance would cost the most since you do not get to use the entire amount. D. It cannot be determined since we do not have the face value of the loan.

Answer 1

Given that two loans have identical face values

Time to maturity = 1 year

For 1st loan, EAR

=[1*(1+ loan rate)/(1- origination free)]-1

= 1*1.083/(1-0.0096)-1

=(1.083/ 0.9904) -1 = 0.0935 = 9.35%

EAR of first loan = 9.35%

For 2nd loan, EAR

= [1*(1+ loan rate)/(1- compensating balance)]-1

=1*1.083/(1-0.053)-1

= (1.083/0.947) -1 = 0.143611 = 14.36%

EAR of second loan = 14.36%

From the above, we can see that second loan has highest EAR

This is because

The loan with the compensating balance would cost the most since you do not get to use the entire amount.