Question

Summit Record Company is negotiating with two banks for a $139,000 loan. Fidelity Bank requires a compensating balance of 14 percent, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a compensating balance of 7 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 $139,000 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=

b. Recompute the effective cost of interest, assuming that Summit ordinarily maintains $19,460 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=

Answer 1

Fidelity Bank:

Interest = Interest rate ×Principal

= .12 ×$139,000= $16,680

Compensating balance = C ×Principal

= .14 ×$139,000= $19,460

Effective rate of interest = (2 ×Annual number of payments ×Interest) / [(Total number of payments + 1) ×Principal]

= (2 ×4 ×$16,680) / [(4 + 1) ×($139,000 −16,680 - 19,460)]

=$133,440 / $514,300 = 0.2595, or 25.95%

Southwest Bank:

Interest = Interest rate ×Principal

= .12 ×$139,000= $16,680

Compensating balance = C ×Principal

= .07 ×$139,000= $9,730

Effective rate of interest = (2 ×Annual number of payments ×Interest) / [(Total number of payments + 1) ×Principal]

= (2 ×12 ×$16,680) / [(12 + 1) ×($139,000 −16,680 - 9,730)]

=$400,320 / $1,463,670 = 0.2735, or 27.35%

Interest = Interest rate ×Principal

= .12 ×$139,000= $16,680

Compensating balance = C ×Principal

= .14 ×$139,000= $19,460

Effective rate of interest = (2 ×Annual number of payments ×Interest) / [(Total number of payments + 1) ×Principal]

= (2 ×4 ×$16,680) / [(4 + 1) ×($139,000 −16,680 - 19,460)]

=$133,440 / $514,300 = 0.2595, or 25.95%

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 × $16,680) / [(4 + 1) × ($139,000 − 16,680)]

= $133,440 / $611,600 = 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 × $16,680) / [(12 + 1) × $139,000]

= $400,320 / $1,807,000 = 0.2215, or 22.15%