## What is the amortization method for the effective interest rate?

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

Key points to remember:

• The effective interest rate method is used to discount, or write off, a bond.
• The amount of the bond discount is amortized as interest expense over the life of the bond. As the book value of a bond increases, the amount of interest expense increases.
• The effective interest rate method takes into account the impact of the purchase price of the bond rather than recognizing only its nominal or nominal value.
• For lenders or investors, the effective interest rate reflects the real return much better than the nominal rate.
• For borrowers, the effective interest rate provides a better visualization of costs.
• Unlike the real interest rate, the effective interest rate does not take inflation into account.

## Understanding the effective interest rate method

The preferred method for amortizing (or progressively expensing the discount on) a bond is the effective interest rate method. Under this method, the amount of interest expense in a given accounting period correlates with the carrying amount of a bond at the start of the accounting period. Therefore, as the book value of a bond increases, the amount of interest expense increases.

When a discounted bond is sold, the amount of the discount on the bond must be amortized as interest expense over the life of the bond. When using the effective interest rate method, the debit amount from the bond discount payable is transferred to the interest account. Therefore, amortization causes interest expense in each accounting period to be greater than the amount of interest paid in each year of the life of the obligation.

For example, suppose 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 of \$ 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 rate amortization method increases the carrying amount of the obligation from \$ 95,000 on January 1, 2017 to \$ 100,000 prior to maturity of the obligation. The issuer must pay interest of \$ 3,000 for every six months that the bond is outstanding. The cash account is then credited with \$ 3,000 on June 30 and December 31.

### Assessment of the interest of a bond

The effective interest rate method is used when measuring the interest generated by a bond because it takes into account the impact of the purchase price of the bond rather than recognizing only the nominal value.

While some bonds pay no interest and only earn income at maturity, most offer a fixed annual rate of return, called a coupon rate. The coupon rate is the amount of interest generated by the bond each year, expressed as a percentage of the face value of the bond.

### The face value of a bond

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

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

If the bond in the example above sells for \$ 800, the interest payments of \$ 60 that it generates each year is a higher percentage of the purchase price than the coupon rate of 6%. Although the face value and the coupon rate are fixed at issue, the bond pays a higher interest rate from the investor’s point of view. The effective interest rate on this bond is \$ 60 / \$ 800 or 7.5%.

If the central bank cut interest rates to 4%, this bond would automatically become more valuable due to its higher coupon rate. If this bond were then sold for \$ 1,200, its effective interest rate would drop to 5%. While still higher than newly issued 4% bonds, the increase in the sale price partially offsets the effects of the rate hike.

### Justification of the effective interest rate

In accounting, the effective interest rate method examines the relationship between the carrying amount of an asset and the related interest. In the area of ​​loans, the effective annual interest rate may refer to an interest calculation in which compounding occurs more than once a year. In finance and capital economics, the effective interest rate of an instrument can refer to the return based on the purchase price.

All of these terms are related in one way or another. For example, effective interest rates are an important part of the effective interest rate method.

The effective interest rate of an instrument can be compared to its nominal interest rate or to its real interest rate. The effective rate takes into account two factors: the purchase price and the composition. For lenders or investors, the effective interest rate reflects the real return much better than the nominal rate. For borrowers, the effective interest rate provides a better visualization of costs. In other words, the effective interest rate is equal to the nominal return on the real principal investment. In terms of bond accounting, the effective interest rate is the same as the yield on a bond at the date of issue.

An interest-bearing asset also has a higher effective interest rate as compounding occurs. For example, an asset compounded with interest annually has a lower effective rate than an asset compounded monthly.

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

The effective interest rate is a more precise figure of the actual interest earned on an investment or the interest paid on a loan.

### The advantage of effective interest rates

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

The calculation of the effective interest rate is commonly used in relation to the bond market. The calculation provides the actual interest rate returned over a given period, based on the actual carrying amount of a financial instrument at the start of the period. If the book value of the investment decreases, the interest earned will also decrease.

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

### Real interest earned

The calculation of the effective interest rate reflects the actual interest earned or paid over a specified period. It is considered preferable to the linear method of calculating premiums or discounts as they apply to bond issues because it is a more precise statement of interest from the start to the end of a chosen accounting period ( the amortization period).

On a period-by-period basis, accountants consider the effective interest rate method to be much more accurate in calculating the impact of an investment on a company’s bottom line. To achieve this increased accuracy, however, the interest rate must be recalculated each month of the accounting period; these additional calculations are a disadvantage of the effective interest rate. If an investor uses the simpler straight-line method to calculate interest, the amount charged each month does not change; it’s the same amount every month.

## Special considerations

Whenever an investor buys, or a financial entity such as the US Treasury or a corporation sells, a bond instrument for a price different from the face value of the bond, the actual interest rate earned is different from the the bond’s stated interest rate. The bond may trade at a premium or at a discount to its face value. In both cases, the real effective interest rate differs from the indicated rate. For example, if a bond with a face value of \$ 10,000 is purchased for \$ 9,500 and the interest payment is \$ 500, the effective interest rate earned is not 5% but 5. 26% (\$ 500 divided by \$ 9,500).

For loans such as a home loan, the effective interest rate is also called the annual percentage rate. The rate takes into account the effect of compound interest as well as any other costs the borrower assumes for the loan.

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