Summit Record Company is negotiating with two banks for a $118,000 loan. Fidelit
ID: 2740607 • Letter: S
Question
Summit Record Company is negotiating with two banks for a $118,000 loan. Fidelity Bank requires a compensating balance of 16 percent, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a compensating balance of 8 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 $118,000 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 $18,880 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.)
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.)
Explanation / Answer
a-1. Calculation of effective rate of interest
Fidelity Bank:
Interest =Interest rate × Principal
= 0.09 × $118,000 =$10620
Compensating balance = C × Principal
= 0.16 × $118,000 = $18880
Effective rate of interest = (2 × Annual number of payments × Interest) / [(Total number of payments + 1) × Principal]
= (2 × 4 × $10,620) / [(4 + 1) × ($118,000 10620 18880)]
= $84960 / $442500 = 0.192, or 19.20%
Southwest Bank:
Interest =Interest rate × Principal
= 0.09 × $118,000 =$10620
Compensating balance = C × Principal
= 0.08 × $118,000 = $9440
Effective rate of interest = (2 × Annual number of payments × Interest) / [(Total number of payments + 1) × Principal]
= (2 × 12 × $10620) / [(12 + 1) × ($118000 9440)]
= $254880 / $1,411280 = .0.1806 or 18.06%
a-2. Summit should select Southwest Bank since its loan has the lower effective interest rate.
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 × $10620) / [(4 + 1) × ($118000 10620)]
= $84960 / $536900 = 0.1582, or 15.82%
Southwest Bank:
Effective rate of interest = (2 × Annual number of payments × Interest) / [(Total number of payments + 1) × Principal]
= (2 × 12 × $10620) / [(12 + 1) × $118,000]
= $254880 / $1534000 = 0.1662, or 16.62%
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 because Fidelity will have the lower effective interest rate.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.