EX 11-3 Evaluate alternative notes

A borrower has two alternatives for a loan: (1) issue a $180,000, 45-day, 10% note or (2) issue a $180,000, 45-day note that the creditor discounts at 10%.

a. Calculate the amount of the interest expense for each option.
b. Determine the proceeds received by the borrower in each situation.
c. Which alternative is more favorable to the borrower? Explain.

Answer:

a. $180,000 × 10% × 45/360 = $2,250 for each alternative.

b.
(1) $180,000 simple-interest note: $180,000 proceeds
(2) $180,000 discounted note: $180,000 – $2,250 interest = $177,750 proceeds

c. Alternative (1) is more favorable to the borrower. This can be verified by comparing the effective interest rates for each loan as follows:  

Situation (1): 10% effective interest rate  
($2,250 × 360/45)/$180,000 = 10%
Situation (2): 10.13% effective interest rate  
($2,250 × 360/45)/$177,750 = 10.13%

The effective interest rate is higher for the second loan because the creditor lent only $177,750 in return for $2,250 interest over 45 days. In the simpleinterest loan, the creditor must lend $180,000 for 45 days to earn the same $2,250 interest.

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