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Summit Record Company is negotiating with two banks for a $104,000 loan
Summit Record Company is negotiating with two banks for a $104,000 loan. Fidelity Bank requires a compensating balance of 22 percent, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a compensating balance of 11 percent, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 10 percent. Compensating balances will be subtracted from the $104,000 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.)
Effective Rate of Interest Fidelity Bank % Southwest Bank %
a-2. Which loan should Summit accept?
0 Southwest Bank 0 Fidelity Bank
b. Recompute the effective cost of interest, assuming that Summit ordinarily maintains $22,880 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.)
Effective Rate of Interest Fidelity Bank . % Southwest Bank . %
c. Does your choice of banks change if the assumption in part b is correct?
O Yes O No
Expert Solution
a-1) Computation of Effective Rate of Interest:
Fidelity Bank:
Interest = Interest rate * Principal
=10% * $104,000
=$10,400
Compensating balance = C * Principal
= 22% * $104,000
= $22,880
Effective Rate of Interest = (2 * Annual number of payments * Interest) / [(Total number of payments + 1) * Principal]
= (2 * 4 * $10,400) / [(4 + 1) * ($104,000 − 10,400− 22,800)]
= $83,200 / $354,000
= 0.2350 or 23.50%
Southwest Bank:
Interest = Interest Rate * Principal
= 10% * $104,000
= $10,400
Compensating Balance= C * Principal
= 11% * $104,000
= $11,440
Effective Rate of Interest = (2 * Annual number of payments * Interest) / [(Total number of payments + 1) * Principal]
= (2 * 12 * $10,400) / [(12 + 1) * ($104,000 − 11,440)]
= $249,600 / $1,203,280
= .2074 or 20.74%
b:
The compensating balance requirement for both banks will be met by the current cash deposits.
Fidelity Bank:
Effective Rate of Interest = (2 * Annual number of payments * Interest) / [(Total number of payments + 1) * Principal]
= (2 * 4 * $10,400) / [(4 + 1) * ($104,000 − $10,400)]
= $83,200 / $468,000
= .0.1778 , or 17.78%
Southwest Bank:
Effective Rate of Interest = (2 * Annual number of payments * Interest) / [(Total number of payments + 1) * Principal]
= (2 * 12 * $10,400) / [(12 + 1) * $104,000]
= $249,600 / $1,352,000
= .1846, or 18.46%
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