An organization needs to borrow a large amount of cash to fund its expansion plan. Which of the following annual interest rates is least expensive?

The least expensive loan is the one with the lowest effective annual rate (EAR). A 7 percent simple interest loan paid at the end of the year has an EAR of exactly 7%, as the borrower has use of the full principal for the entire period. The other options increase the effective cost of borrowing. A compensating balance (A) and discount interest (C) both reduce the amount of usable funds, thereby increasing the EAR. Compounding interest (D) also results in an EAR greater than the stated 7% if the compounding period is more frequent than once a year.

A. The 10% compensating balance reduces the usable loan proceeds, increasing the effective rate to approximately 7.78% (7% interest / 90% of usable funds).
C. With discount interest, the 7% interest is deducted upfront, reducing usable funds and increasing the effective rate to approximately 7.53% (7% interest / 93% of usable funds).
D. Compounding interest more frequently than annually results in an effective annual rate higher than the 7% nominal rate due to interest being earned on previously accrued interest.

1. Brigham

E. F.

& Houston

J. F. (2019). Fundamentals of Financial Management (15th ed.). Cengage Learning. In Chapter 16

"Short-Term Financing

" the text explains how to calculate the effective cost of different short-term credit arrangements. It demonstrates that both compensating balances and discount interest increase the effective rate of a loan above its stated rate (pp. 558-561).

2. Ross

S. A.

Westerfield

R. W.

& Jordan

B. D. (2018). Fundamentals of Corporate Finance (12th ed.). McGraw-Hill Education. Chapter 6

"Understanding and Valuing Bonds

" distinguishes between the stated interest rate and the effective annual rate (EAR)

showing that compounding increases the effective rate. The formula EAR = [1 + (Quoted rate / m)]^m – 1 illustrates that for m > 1

EAR > Quoted rate (p. 175).

3. Bodie

Z.

Kane

A.

& Marcus

A. J. (2018). Investments (11th ed.). McGraw-Hill Education. Chapter 5

"Risk

Return

and the Historical Record

" details the calculation of effective annual rates from annual percentage rates (APRs)

confirming that more frequent compounding leads to a higher EAR (pp. 124-125).