Summit Record Company is negotiating with two banks for a $104,000 loan. Fidelit
ID: 2732891 • Letter: S
Question
Summit Record Company is negotiating with two banks for a $104,000 loan. Fidelity Bank requires a compensating balance of 26 percent, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a compensating balance of 13 percent, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 12 percent. Compensating balances will be subtracted from the $104,000 in determining the available funds in part a.
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.)
Recompute the effective cost of interest, assuming that Summit ordinarily maintains $27,040 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.)
Summit Record Company is negotiating with two banks for a $104,000 loan. Fidelity Bank requires a compensating balance of 26 percent, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a compensating balance of 13 percent, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 12 percent. Compensating balances will be subtracted from the $104,000 in determining the available funds in part a.
Explanation / Answer
FIDELITY BANK:
INTEREST
=INTEREST RATE * PRINCIPAL= 0.12 * $104000
=$12480
COMPENSATING BALANCE
= C * PRINCIPAL
= 0.26 * $104000
= $27040
EFFECTIVE RATE OF INTEREST
= (2 * ANNUAL NUMBER OF PAYMENTS * INTEREST) / [(TOTAL NUMBER OF PAYMENTS + 1) * PRINCIPAL]
= (2 * 4 × $12480) / [(4 + 1) × ($104000 12480 27040)]
= $99840 / $322400
= 0.3097, or 30.97%
SOUTHWEST BANK:
INTEREST
=INTEREST RATE * PRINCIPAL
=0.12 * $104000
=$12480
COMPENSATING BALANCE
= C * PRINCIPAL
= 0.13 * $104000
= $13520
EFFECTIVE RATE OF INTEREST
= (2 * ANNUAL NUMBER OF PAYMENTS * INTEREST) / [(TOTAL NUMBER OF PAYMENTS + 1) × PRINCIPAL]
= (2 * 12 * $12480) / [(12 + 1) * ($104000 13520)]
= $299520 / $1176240
= 0.2546, OR 25.46%
A.2/
SUMMIT SHOUL SELECT SOTHWEST BANK BECAUSE IT HAS ALOWER EFFECTIVE INTEREST AS COMPARE TO FIDILITY BANK.
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 * $12480) / [(4 + 1) * ($104000 12480)]
= $99840 / $457600
=0 .2182, OR 21.82%
SOUTHWEST BANK:
EFFECTIVE RATE OF INTEREST
= (2 * ANNUAL NUMBER OF PAYMENTS * INTEREST) / [(TOTAL NUMBER OF PAYMENTS + 1) * PRINCIPAL]
= (2 * 12 * $12480) / [(12 + 1) * $104000]
= $299520 / $1352000
=0 .2215, OR 22.15%
C./
YES,IF BOTH THE BANKS MAINTAIN COMPONSATING BALANCE THAN FIDILITY BANK SHOULD BE CHOOSEN OVER SOUTH WEST BANK, BECAUSE FIDILITY BANK HAS A LOWER EFFECTIVE INTEREST AS COMPARE TO SOUTH WEST BANK.
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