# Computing The Effective Annual Interest Rate on Loans

Your firm is considering the following three alternative bank loans for $1,000,000:

a) 10% loan paid at year end with no compensating balance

b) 9% loan paid at year end with a 20% compensating balance

c) 6% loan that is discounted with a 20% compensating balance requirement

Assume that you would normally not carry any bank balance that would meet the 20% compensating balance requirement. What is the rate of annual interest on each loan?

© BrainMass Inc. brainmass.com October 25, 2018, 1:52 am ad1c9bdddfhttps://brainmass.com/business/interest-rates/computing-the-effective-annual-interest-rate-on-loans-277909

#### Solution Preview

A compensating balance is a balance kept on deposit with the lender which the borrower does not have use of. However, the compensating balance is considered to be part of the loan and interest is charged on it.

a) The interest due on a 10% loan of $1,000,000 paid at year ...

#### Solution Summary

This solution illustrates how to compute the effective annual interest rate on three loans: a loan with no compensating balance, a loan with a compensating balance, and a loan issued at a discount to face value with a compensating balance.

Heister, Magic Pumpkin, King: break even, effective interest rate, open branch office

1. The Heister Corporation produces class rings for Whatsamadda U. These rings sell for $75.00 each, and cost $35.00 each to produce. Heister has fixed costs of $50,000.

a. Calculate Heister's break-even point.

b. How much profit (loss) will Heister have if it sells 1,000 rings?

c. How much profit (loss) will Heister have if it sells 8,000 rings?

d. Heister's president, J. Circle, expects an annual profit of $100,000. How many rings must be sold to attain this profit?

2. The Magic Pumpkin Limousine Company wants to purchase a car telephone system for one of its automobiles. The telephone vendor has offered to finance the $1,500 purchase over one year in 12 installments, with a total of $140 in interest to be paid on the loan. Magic Pumpkin's bank has offered to finance the purchase with an installment loan, where $155 in interest will be repaid and payments on the loan must be made quarterly. What are the effective interest rates on these loans? Which would you choose and why?

3. King, Inc., a successful Midwest firm, is considering opening a branch office on the west coast. Under normal economic conditions, with a 45% probability of occurring, King can expect to earn a net income of $50,000 per year. In a mini-recession, at 25% probability, King will earn $20,000. In a severe recession, at a 20% probability, King will lose $10,000. There is a slight probability (10%) that King will lose $30,000 if the expansion fails and the branch office must be closed. Should King open a branch office on the west coast?

View Full Posting Details