## Effective interest rate in the context of loans

October 27, 2011

Learn about effective annual interest rate in the context of loans.

## 1. Introduction to effective annual interest rate in context of loans

The effective annual interest rate on loans measures the real (true) cost of credit. The calculation of the effective interest rate varies depending on the type of loan.� Let us looks at various types of loans to see how the effective interest rate is determined.

## 2. Effective annual interest rate on single-payment loans

Single-payment loans are the loans that are paid off on a given date. There are two methods that can be used to calculate the effective annual interest rate on single-payment loans (refer to the table below).

Illustration 1: Effective annual interest rates (EAR) on single-payment loans

 Simple interest method Interest is calculated on the amount borrowed. Stated and effective interest rates are the same. EAR = Interest � Proceeds When a loan requires a compensating balance: Proceeds = Principle x Proceeds Percentage Proceeds Percentage =100% - Compensating Balance Percentage Discount method Interest is deducted from the amount of the loan. Borrower prepays the finance charge. EAR = Interest � (Principal � Interest) When a loan requires a compensating balance: Proceeds = Principal x Proceeds Percentage - Interest Proceeds percentage =100% - Compensating Balance Percentage

Let us look at a few examples to see how the effective annual interest rate is calculated for single-payment loans.

Single-payment Loans � Example 1:

Company ABC can take a \$100,000 loan from Bank X or Bank Y. Bank X can give the one-year loan at 10% paid at maturity, while Bank Y can lend on a discounted basis at a 10% interest rate. Which bank charges a lower effective annual interest rate (EAR)?

EAR (Bank X) = 0.10

 EAR (Bank Y) = \$100,000 x 0.10 = 0.1111 \$100,000 x (1 � 0.10)

As we can see, Company ABC should take the loan from Bank X as it charges the lower EAR.

Single-payment Loans � Example 2:

Company ABC took a \$500,000 loan at a 10% interest rate from Bank X. The interest is due at maturity. Bank X requires a 20% compensation balance. What is the effective annual interest rate?

 EAR = Principal x Interest Rate Principal x (1 � compensating balance %)
 EAR = \$500,000 x 0.10 = 0.1250 \$500,000 x (1 � 0.20)

## 3. Effective annual interest rate on a line of credit

Under a line of credit, a borrower can lend money from a lending institution (e.g. bank) on a recurring basis up to a certain amount. The borrower might be required to maintain a deposit that does not earn interest. Such a deposit is called a compensating balance that is usually presented as a percentage of the loan. If a compensating balance is placed on the unused portion of the line of credit, the interest rate will be smaller.

To calculate the effective annual interest rate on a line of credit, the following formula can be used:

 �EAR = Principal x Interest Rate Principal � Compensating Balance

Line of Credit � Example 1:

Company ABC has a \$100,000 line of credit at Bank Z. The company must maintain the following compensating balances: 15% on outstanding loan and 10% on the unused portion of the line of credit. The company borrowed \$60,000. The interest rate on the loan is 12%. What is the effective annual interest rate?

The required deposit equals: \$60,000 x 15% + \$40,000 x 10% = \$13,000

 EAR = \$60,000 x 0.12 = 0.1532 \$60,000 � \$13,000

The effective interest rate on this loan (on a line of credit) is 15.32%.

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