Question

Summit Record Company is negotiating with two banks for a $157,000 loan. Fidelity Bank requires a compensating balance of 24 percent, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a compensating balance of 12 percent, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 9 percent. Compensating balances will be subtracted from the $157,000 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 $37,680 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

Answer

a.1

Fidelity Bank = 21.49%

Southwest Bank = 18.88%

a.2

Southwest Bank

b.

Fidelity = 15.82%

Southwest Bank = 16.61%

c. YES

Explanation

a.1

Fidelity Bank

Effective interest rate =

Numerator = 2 * 4 (Since Quarter) * 14,130 (9% of 157,000)

Deniominator = 157000 - 37,680 (28% of 157000) - 9% * (4+1) Quarter

=

113,040 02149 525, 950

= 21.49%

Southwest Bank

Effective interest rate = $\frac{2 * 12 *14,130 }{(157,000 - 18,840) * (12+1)}$

Numerator = 2 * 12 (Since 12 installments ) * 14,130 (9% of 157,000)

Deniominator = 157000 - 18,840 (12% of 157000) * (12+1) 12 Installments

=  $\frac{339,120}{1,796,080} = 0.1888$

= 18.88%

a.2 Choose Southwest Bank since it has the lowest effective interest rate.​

b.

The numerators stay the same as in part (a) but the denominator increases to reflect the use of more money because compensating balances are already maintained at both banks.

Fidelity Bank

Effective interest rate = $\frac{2 * 4 *14,130 }{(157,000 - 14,130) * (4+1)}$

$\frac{113,040}{714,350} = 0.1582$

= 15.82%

Southwest Bank

Effective interest rate = $\frac{2 * 12 *14,130 }{(157,000 ) * (12+1)}$

= $\frac{339,120}{2,041,000} = 0.1661$

=16.61%

c) Yes. If compensating balances are maintained at both banks in the normal course of business, then Fidelity Bank should be chosen over Southwest Bank. The effective cost of its loan will be less​