# How to compute loan interest

## How to calculate the effective interest rate

The effective interest rate is the usage rate that a borrower actually pays on a loan. This rate may vary from the rate stated on the loan document, based on an analysis of several factors; a higher effective rate might lead a borrower to go to a different lender. These factors are:

- The number of times the debt is compounded during the year
- The actual amount of interest paid
- The amount the investor paid for the debt

When only incorporating the impact of compounding on the interest rate, the steps required to calculate the effective interest rate are:

- Locate in the loan documents the compounding period. It is likely to be either monthly, quarterly, or annually.
- Locate the stated interest rate in the loan documents.
- Enter the compounding period and stated interest rate into the effective interest rate formula, which is:

r = (1 + i/n)^n-1

Where:

r = The effective interest rate

i = The stated interest rate

n = The number of compounding periods per year

For example, a loan document contains a stated interest rate of 10% and mandates

quarterly compounding. By entering this information into the effective interest rate formula, we arrive at the following effective interest rate:

(1 + 10%/4)^4-1 = 10.38% Effective interest rate

There are other circumstances that can alter the interest rate paid to an even greater extent. Consider the following additional factors:

*Additional fees*. The borrower may pay additional fees that are disguised forms of interest expense. These fees are worth including in the calculation if they are material.*Altered amount lent*. If the investor does not agree that the market interest rate matches the stated interest rate to be paid by the borrower, the investor can bid less or more than the face amount to acquire the debt. Thus, if the market interest rate is higher than the face amount of the debt instrument, the borrower pays less for the debt, thereby creating a higher effective yield. Conversely if the market interest rate is lower than the face amount of the debt instrument, the borrower is willing to pay more for the debt.

Conducting a complete analysis of the effective interest rate could be quite illuminating for a borrower, who may find that a prospective borrowing arrangement should be avoided.

**Related Topics**

Category: Credit

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