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 singlepayment loans
Singlepayment 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 singlepayment loans (refer to the table below).
Illustration 1: Effective annual interest rates (EAR) on singlepayment loans
Simple interest 

EAR = Interest χ Proceeds 

When a loan requires a compensating balance: Proceeds = Principle x Proceeds Percentage Proceeds Percentage =100%  Compensating Balance Percentage 

Discount method 

EAR = Interest χ (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 singlepayment loans.
Singlepayment Loans Example 1:
Company ABC can take a $100,000 loan from Bank X or Bank Y. Bank X can give the oneyear 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.
Singlepayment 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%.