# What is the effective interest method of amortization?

The effective interest method is an accounting practice used for discounting a bond. This method is used for bonds sold at a discount; the amount of the bond discount is amortized to interest expense over the bond's life.

## Explaining the Effective Interest Rate Method

The preferred method for amortizing (or gradually writing off) a discounted bond is the effective interest rate method or the effective interest method. Under the effective interest rate method, the amount of interest expense in a given accounting period correlates with the book value of a bond at the beginning of the accounting period. Consequently, as a bond's book value increases, the amount of interest expense increases.

When a discounted bond is sold, the amount of the bond's discount must be amortized to interest expense over the life of the bond. When using the effective interest method, the debit amount in the discount on bonds payable is moved to the interest account. Therefore, the amortization causes interest expense in each period to be greater than the amount of interest paid during each year of the bond's life.

For example, assume a 10-year $100,000 bond is issued with a 6% semi-annual coupon in a 10% market. The bond is sold at a discount for $95,000 on January 1, 2017. Therefore, the bond discount of $5,000, or $100,000 less $95,000, must be amortized to the interest expense account over the life of the bond.

The effective interest method of amortization causes the bond's book value to increase from $95,000 on January 1, 2017 to $100,000 prior to the bond's maturity. The issuer must make interest payments of $3,000 every six months the bond is outstanding. The cash account is then credited $3,000 on June 30 and December 31.

## The Effective Interest Rate Method and Bond Pricing

The effective interest method is used when evaluating the interest generated by a bond because it considers the impact of the bond purchase price rather than accounting only for par value.

Though some bonds pay no interest and generate income only at maturity, most offer a set annual rate of return, called the coupon rate. The coupon rate is the amount of interest generated by the bond each year, expressed as a percentage of the bond's par value.

## Par value

Par value, in turn, is simply another term for the bond's face value, or the stated value of the bond at the time of issuance. A bond with a par value of $1,000 and a coupon rate of 6% pays $60 in interest each year.

A bond's par value does not dictate its selling price. Bonds that have higher coupon rates sell for more than their par value, making them premium bonds. Conversely, bonds with lower coupon rates often sell for less than par, making them discount bonds. Because the purchase price of bonds can vary so widely, the actual rate of interest paid each year also varies.

If the bond in the above example sells for $800, then the $60 interest payments it generates each year actually represent a higher percentage of the purchase price than the 6% coupon rate would indicate. Though both the par value and coupon rate are fixed at issuance, the bond actually pays a higher rate of interest from the investor's perspective. The effective interest rate of this bond is $60 / $800, or 7.5%.

If the central bank reduced interest rates to 4%, this bond would automatically become more valuable because of its higher coupon rate. If this bond then sold for $1,200, its effective interest rate would sink to 5%. While this is still higher than newly issued 4% bonds, the increased selling price partially offsets the effects of the higher rate.

## Rationale behind Effective Interest Rate Method

In accounting, the effective interest method examines the relationship between an asset's book value and related interest. In lending, the effective annual interest rate might refer to an interest calculation wherein compounding occurs more than once a year. In capital finance and economics, the effective interest rate for an instrument might refer to the yield based on purchase price.

All of these terms are related in some way. For example, effective interest rates are an important component of the effective interest method.

An instrument's effective interest rate can be contrasted with its nominal interest rate or real interest rate. The effective rate takes two factors into consideration: purchase price and compounding. For lenders or investors, the effective interest rate reflects the actual return far better than the nominal rate. For borrowers, the effective interest rate shows costs more effectively.

Put another way, the effective interest rate is equal to the nominal return relative to the actual principal investment. In terms of bonds, this is the same as the difference between coupon rate and yield.

An interest-bearing asset also has a higher effective interest rate as more compounding occurs. For example, an asset that compounds interest yearly has a lower effective rate than an asset with monthly compounding.

Unlike the real interest rate, the effective interest rate does not take inflation into account. If inflation is 1.8%, a Treasury bond (T-bond) with a 2% effective interest rate has a real interest rate of 0.2%, or the effective rate minus the inflation rate.

## Advantages of Using An Effective Interest Rate Figure

The primary advantage of using the effective interest rate figure is simply that it is a more accurate figure of actual interest earned on a financial instrument or investment, or of actual interest paid on a loan, such as a home mortgage.

The effective interest rate calculation is commonly used with regard to the bond market. The calculation provides the real interest rate returned in a given time period, based on the actual book value of a financial instrument at the beginning of the time period. If the book value of the investment declines, then the actual interest earned will decline as well.

Investors and analysts often use effective interest rate calculations to examine premiums or discounts related to government bonds, such as the 30-year U.S. Treasury bond, although the same principles apply to trading corporate bonds. When the stated interest rate on a bond is higher than the current market rate, then traders are willing to pay a premium over the face value of the bond. Conversely, whenever the stated interest rate is lower than the current market interest rate for a bond, the bond trades at a discount to its face value.

## Actual Interest Earned

The effective interest rate calculation reflects actual interest earned or paid over a specified time frame. It is considered preferable to the straight-line method of figuring premiums or discounts as they apply to bond issues, because it is a more accurate statement of interest from the beginning to the end of a chosen accounting period (the amortization period).

On a period-by-period basis, accountants regard the effective interest method as far more accurate for calculating the impact of an investment on a company's bottom line.

To obtain this increased accuracy, however, the interest rate must be recalculated every month of the accounting period; these extra calculations are a disadvantage of using the effective interest rate. If an investor uses the simpler straight-line method to calculate interest, then the amount charged off each month doesn't vary; it is the same amount every month.

## The Bottom Line

Whenever an investor buys, or a financial entity such as the U.S. Treasury or a corporation sells, a bond instrument for a price that is different from the bond's face amount, then the actual interest rate being earned is different from the bond's stated interest rate. The bond may be trading at a premium or at a discount to its face value. In either case, the actual effective interest rate differs from the stated rate. For example, if a bond with a face value of $10,000 is purchased for $9,500 and the interest payment is $500, then the effective interest rate being earned is not 5%, but 5.26% ($500 divided by $9,500).

When it comes to loans such as a home mortgage, the effective interest rate is also known as the annual percentage rate. It takes into account the effect of compounding interest, along with all other costs that the borrower pays for the loan.

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