Summit Record Company is negotiating with two banks for a $100,000 loan. Fidelit

Question

Summit Record Company is negotiating with two banks for a $100,000 loan. Fidelity Bank requires a 20 percent compensating balance, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a 10 percent compensating balance, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 9 percent.




(a) Calculate the effective interest rate for Fidelity Bank and Southwest Bank. (Round your answers to 2 decimal places. Omit the "%" sign in your response.)

Effective rate:
Fidelity Bank= %
Southwest Bank= %


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(b) Recompute the effective cost of interest, assuming that Summit ordinarily maintains $20,000 at each bank in deposits that will serve as compensating balances. (Round your answers to 2 decimal places. Omit the "%" sign in your response.)

Effective rate:

Fidelity Bank= %
Southwest Bank= %


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Explanation / Answer

(a)

Fidelity Bank

Compensating balance = 20 % of 100,000 = 0.2 * 100,000 = 20,000

No. of payments = 4 (since only quarterly payments are required.)

discounted loan  rate = 9 % of 100,000 = 9,000

Effective interest rate = 2 * No.of payments * loan rate/(Total loan - comnsating balance -loan rate) * ( no. of payments +1)     --------------(1)

Effective intereset rate = 2 * 4 *9000/((100,000 - 20,000 - 9000) * ( 4 + 1)) = 20.28 %

Southwest Bank

Compensating balance = 10 % of 100,000 = 0.1 * 100,000 = 10,000

No. of payments = 12 (since only monthly payments are required.)

loan  rate = 9 % of 100,000 = 9,000

Here there is no dicounting. so,

Effective interest rate = 2 * No.of payments * loan rate/(Total loan - comnsating balance) * ( no. of payments +1)   --------------(2)

Effective intereset rate = 2 * 12 *9000/((100,000 - 10,000) * ( 12 + 1)) = 18.46 %

(b)

If the company normally maintains 20,000 dollars that serve as compensating balance then,

In the above (1) and (2) equations we use compensating balance = 0

For 

Fidelity bank effective interest rate = 2 * 4 *9000/((100,000 - 0 - 9000) * ( 4 + 1)) = 15.82 %

For

South west bank effective interest rate =  2 * 12 *9000/((100,000 - 0) * ( 12 + 1)) = 16.62 %

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