 # Effective Interest Rate By Yuriy Smirnov Ph.D.

## Definition

The concept of effective interest rate is widely used in finance to assess the interest expense of debt financing or interest income for financial assets. Moreover, IFRS (International Financial Reporting Standards) require that the effective interest rate method be used to assess financial instruments that are accounted for at amortized costs, to recognize financial incomes or financial expenses, and to recognize the impairment of a financial asset on the basis of its present value of estimated cash flows.

The reason to do so is that a nominal or stated interest rate often does not include all expenses related to financial instruments. The most common factors that cause a different effective interest rate than a nominal one are as follows:

• Number of compounding periods during a year
• Actual amount of interest expense
• Extra fees

## Formula

The effective interest rate is a very important concept in finance when it is necessary to compare different short-term financial instruments, e.g., bank loans, lines of credit, commercial papers and bills, T-bills, and certificates of deposit. Different financial instruments may have unequal maturity periods and compound interest in a different way. We need a metric to compare them on an annual basis, which is why it is also called annual equivalent rate.

### Financial assets

We should use the following equation to assess the efficient annual interest rate for financial assets that mature in less than 12 months: where r is a nominal annual interest rate, and n is a number of compounding periods (e.g., if interest compounds monthly, n equals 12).

### Short-term loans

If interest is paid on a collecting basis, the effective interest rate for loans is as follows:

 EIR = Interest Expense × T Loan Amount t

where T is the number of days in a year, which can be 365 or 360, and t is the number of days a loan is outstanding.

If interest is paid on a discount basis, the formula above should be rewritten as follows:

 EIR = Interest Expense × T Loan Amount - Interest Expense t

We should take into account the following factors when calculating the effective interest rate:

1. Extra fees. They are hidden interest expense by their nature.
2. Terms and conditions affecting the amount of usable funds. For example, the compensating balance requirement reduces the amount of usable funds.

In such a case, the formulas above should be adjusted as follows:

If interest is charged on a collecting basis, the formula is:

 EIR = Interest Expense + Extra Fees × T Loan Amount - Compensating Balance t

If interest is paid on a discount basis, the formula should be modified as follows:

 EIR = Interest Expense + Extra Fees × T Loan Amount - Interest expense - Compensating Balance t

## Calculation examples

### Example 1

Assume that an investor considers buying a commercial bill for \$96,550 that matures in 4 months. The face value of a bill is \$100,000. The calculation of the effective interest rate is as follows:

Interest income = \$100,000 - \$96,550 = \$3,450

 Interest rate per 4 months = \$3,450 = 3.573% \$96,550

Effective annual interest rate = (1 + 0.03573)12/4 - 1 = 11.107%

Please note that we took into account the effect of compounding!

### Example 2

GFL Ltd. Company is looking for a bank loan to finance its working capital needs. Now the company’s management is considering the following offer:

• The amount of the loan is \$100,000
• The loan has a term of 180 days
• The interest is paid on a collecting basis at a nominal interest rate of 12% per annum
• The establishment fee is \$500
• The compensating balance is \$15,000
 Interest expense = \$100,000 × 12% × 180 = \$5,917.81 365
 Efficient annual interest rate = \$5,917.81 + \$500 × 365 = 15.310% \$100,000 - \$15,000 180

### Example 3

Tristan Inc. has a bank loan. The terms and conditions are as follows:

• The amount of the loan is \$250,000
• The loan has a term of 240 days
• The interest is paid on a discount basis at an annual interest rate of 15%
• The establishment fee is 1% of the loan amount
• The compensating balance is \$50,000
 Discount rate = 15% × 240 = 9.863% 365
 Interest expense = \$250,000 - \$250,000 = \$22,443.86 1 + 0.09863

Establishment fee = \$250,000 × 1% = \$2,500

 Efficient annual interest rate = \$22,443.86 + \$2,500 × 365 = 21.365% \$250,000 - \$22,443.86 - \$50,000 240