Question

Summit Record Company is negotiating with two banks for a $147,000 loan. Fidelity Bank requires a compensating balance of 30 percent, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a compensating balance of 15 percent, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 8 percent. Compensating balances will be subtracted from the $147,000 in determining the available funds in part a.
  
a-1. Calculate the effective interest rate for Fidelity Bank and Southwest Bank. (Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.)
  

  
a-2. Which loan should Summit accept?
  

	Southwest Bank
	Fidelity Bank

b. Recompute the effective cost of interest, assuming that Summit ordinarily maintains $44,100 at each bank in deposits that will serve as compensating balances. (Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.)
  

  
c. Does your choice of banks change if the assumption in part b is correct?
  

	Yes
	No

Answer 1

a-1
Calculation of effective interest rate for Fidelity bank
Calculation of interest expense
Interest expense	Interest rate*Loan amount
Interest expense	0.08*147000
Interest expense	$11,760
Compensation balance	C*Principal
Compensation balance	0.30*147000
Compensation balance	$44,100
Effective rate of interest	(2*Number of payments per year*Interest amount per period)/((Number of payments+1)*Principal)
Effective rate of interest	(2*4*11760)/((4+1)*(147000-11760-44100)
Effective rate of interest	94080/455700
Effective rate of interest	20.65%
Calculation of effective interest rate for Southwest company
Calculation of interest expense
Interest expense	Interest rate*Loan amount
Interest expense	0.08*147000
Interest expense	$11,760
Compensation balance	C*Principal
Compensation balance	0.15*147000
Compensation balance	$22,050
Effective rate of interest	(2*Number of payments per year*Interest amount per period)/((Number of payments+1)*Principal)
Effective rate of interest	(2*12*11760)/((12+1)*(147000-22,050)
Effective rate of interest	282240/1624350
Effective rate of interest	17.38%
a-2
Summit should accept southwest bank loan due to lower effective interest rate
b.
The compensating balance is maintain by the company and therefore the new effective interest rate would be
Fidelity bank
Effective rate of interest	(2*Number of payments per year*Interest amount per period)/((Number of payments+1)*Principal)
Effective rate of interest	(2*4*11760)/((4+1)*(147000-11760)
Effective rate of interest	94080/676200
Effective rate of interest	13.91%
Southwest bank
Effective rate of interest	(2*Number of payments per year*Interest amount per period)/((Number of payments+1)*Principal)
Effective rate of interest	(2*12*11760)/((12+1)*147000
Effective rate of interest	282240/1911000
Effective rate of interest	14.77%
c.
Yes, in this case fidelity bank would be preferred as the effective rate of interest is lower than southwest bank.