Effective Interest Method

# Effective Interest Method

At 5 percent interest, the bond will pay \$100 per year in interest. In microfinance, EIR is a less useful calculation than APR when calculating the cash cost of borrowing . The EIR, however, assigns a time value to money, regardless of whether it is charged in cash, and is therefore conceptually more complete. EIR is the standard method of interest calculation in the European Union, and interest rates on all consumer loans in the EU must be disclosed in this format. The straight-line method does not reflect the reality of the transaction. GAAP but only if the reported results are not materially different from those derived using the effective rate method. If interest is then recognized each period based on this same set of variables, the resulting numbers will reconcile.

• In such a scenario difference between the amount paid and the book value of the bond is a discount and is amortized over the life of the bond.
• Therefore, the effective interest rate for the quoted investment is 10.25%.
• In addition, it would record premium amortization of \$1,000 per year (\$10,000 in premium divided by the 10-year life of the bond).
• Second, divide the result by the number of bond payments remaining before the bond matures.
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• Each bond has a face value, which is the amount of principal the bond issuer will pay back to the bondholder when the bond matures.
• Conversely, bonds typically sell at a discount to their face value when the bond’s stated interest rate is less than prevailing market rates.

It received \$91,800 cash and recorded a Discount on Bonds Payable of \$8,200. This amount will need to be amortized over the 5-year life of the bonds. Using the same format for an amortization table, but having received \$91,800, interest payments are being made on \$100,000. For example, assume that \$500,000 in bonds were issued at a price of \$540,000 on January 1, 2019, with the first annual interest payment to be made on December 31, 2019. Assume that the stated interest rate is 10% and the bond has a four-year life. If the straight-line method is used to amortize the \$40,000 premium, you would divide the premium of \$40,000 by the number of payments, in this case four, giving a \$10,000 per year amortization of the premium.

## Effective Interest Method Of Amortization

Although mechanically different, the liability is still shown as \$17,800. The \$1,477.50 debit to Premium on Bonds Payable reduces the carrying value of the bond payable because remember, bonds payable is a Credit account and any debit to it reduces its carrying value. The annual percentage rate is calculated in the following way, where i is the interest rate for the period and n is the number of periods.

In this lesson, we will learn how to calculate holding period returns and how to annualize them. Several formulas will be presented with examples that work through each type of return. Financial assets are resources owned by people or organizations that have monetary value derived from a contractual claim. Learn more about the three main types of financial assets, such as money, stocks, and bonds. The carrying value of the bonds at the end of the period by the effective interest rate. The carrying value of the bonds at the beginning of the period by the effective interest rate. Accounting standards mostly allow only the effective interest method for amortization of discount/premium and transaction costs.

## Amortization

Suppose 5-year \$ 100,000 bond is issued with a 9% semiannual coupon in a 10% market \$ 96,149 in Jan’17 with interest payout in June and January. The effective interest rate calculation is commonly used in relation to the bond market. The calculation provides the real interest rate returned in a given period, based on the actual book value of a financial instrument at the beginning of the period. If the book value effective interest amortization of the investment declines, then the interest earned will decline also. If the bond in the above example sells for \$800, then the \$60 interest payments it generates each year represent a higher percentage of the purchase price than the 6% coupon rate would indicate. Although both the par value and coupon rate are fixed at issuance, the bond pays a higher rate of interest from the investor’s perspective.

The initial journal entry to record the issuance of the bonds, and the final journal entry to record repayment at maturity would be identical to those demonstrated for the straight-line method. However, each journal entry to record the periodic interest expense recognition would vary and can be determined by reference to the preceding amortization table. 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, the actual interest rate 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.

Accrual accounting is the most common method used by businesses. Define accrued expenses and revenues, explore the types of accrued expenses and revenues, and examine practical examples of these two concepts. Loanable funds are the savings available in an economy that can be used to provide loans to individuals and businesses.

## 1 Effective Interest Rate Method For Deferred Financing Cost Amortization

The contra account is reduced so the net liability balance increases. Thus, overall reporting of the interest and the liability is not impacted by the method used in recording the issuance of the bond. Prepare journal entries for a zero-coupon bond using the effective rate method. Cash \$15,000 Entry to record bond interest expense for 2009 and amortization for premium on bonds payable. The straight-line method allocates a fixed portion of the bond discount or premium each interest period to adjust the interest payment to interest expense.

Under the effective interest method, a constant interest rate—equal to the market rate at the time of issue—is used to calculate the periodic interest expense. The critical observation to make is that the straight line method is a much more simple calculation.

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Thus, if the book value of a financial instrument decreases, so too will the amount of related interest; if the book value increases, so too will the amount of related interest. This method is used to account for bond premiums and bond discounts. A bond premium occurs when investors are willing to pay more than the face value of a bond, because its stated interest rate is higher than the prevailing market interest rate.

## How Can I Calculate The Carrying Value Of A Bond?

Unlike the real interest rate, the effective interest rate does not account for inflation. For borrowers, the effective interest rate shows costs more effectively. The most common and comparable interest rate is the APR , also called nominal APR, an annualized rate which does not include compounding. The United States Truth in Lending Act requires disclosure using the APR, and it is used as a standard rate in many other countries. Has been established by the parties, the actual price of the bond is simply a mathematical computation. Calculate the price of a zero-coupon bond and list the variables that affect this computation.

The price is the future cash payments with the negotiated rate of interest removed. If the investor pays \$17,800 today and the debtor returns \$20,000 in two years, the extra \$2,200 is the interest. And, mathematically, that extra \$2,200 is exactly equal to interest at 6 percent per year. Upon recognition of finance leases, lessors record the difference between the gross investment and the net investment as unearned interest income to be recognized as revenue and amortized over the lease term using the EIR method. As illustrated, the \$1,007,000, 5-year, 12% bonds issued to yield 14% were sold at a price of \$92,976, or at a discount of \$7,024. The table below shows how this discount is amortized using the effective interest method over the life of the bond. The cash interest payment is still the stated rate times the principal.

Normal journal entries will be passed on the issuance of bonds, accrual, and payment of interest, payment of principal amount at maturity. Using the straight-line amortization method, accountants transfer an equal amount from the bond discount or premium account over to the interest expense account each payment period. For bond discounts, accountants add onto the interest expense balance each month, to account for the additional expense of selling a bond at a discount and repaying it at face value.

## What Is The Effective Interest Rate Formula?

A bond discount occurs when investors are only willing to pay less than the face value of a bond, because its stated interest rate is lower than the prevailing market rate. The price of the bond is determined by computing the present value of the required cash flows using the effective interest rate negotiated by the two parties. Present value represents the principal of the debt with all future interest mathematically removed.

Let’s now consider how to use the effective interest method for both the discount and premium cases. Over the life of the bond, this percentage interest rate continues to decrease until 2 January 2025, when it reaches 6.7% (or \$6,702 / \$99,294). Therefore, the interest rate is constant over the term of the bond, but the actual interest expense changes as the carrying value of the bond changes. To calculate premium amortization, we take the amount of cash interest (\$9,000) and subtract the interest expense (\$8,536.81) to get premium amortization of \$463.19. Advance your career in investment banking, private equity, FP&A, treasury, corporate development and other areas of corporate finance. The effective interest method is used to discount, or write off, a bond. EIR can be calculated using the above formula with a financial calculator (or any calculator which has an exponent function) or using a basic spreadsheet program like Excel.

In the straight line amortization method, the bond’s carrying value changes each period while the bond interest expense each period remains the same. This displays a changing interest rate when the carrying value fluctuates each period while interest remains the same. Thus, the accounting handbooks advise to only use this rule when the results do not differ significantly from the effective interest method.

Subtract the interest from the payment of \$23,097.48 to find \$18,097.48 is applied toward the principal (\$100,000), leaving \$81,902.52 as the ending balance. In year 2, \$81,902.52 is charged 5% interest (\$4,095.13), but the rest of the 23,097.48 payment goes toward the loan balance. Figure 13.7 shows an amortization table for this \$10,000 loan, over five years at 12% annual interest.

Total interest reported for this zero-coupon bond is equal to the difference between the amount received by the debtor and the face value repaid. Both of the accounting problems have been resolved through use of the effective rate method.

Let us take the example of an investment with the stated rate of interest of 10%. Calculate the effective interest rate if the investment is to be compounded twice a year.

## Effective Interest Rate Method Vs Straight

Interest expense is the amount or cost incurred by the borrower for using the funds obtained from debt sources such as loans, bonds, notes payable, etc. The stated interest rate is applied to the face value of the asset/liability to determine interest receipt/payment. In other words, the effective interest rate is the internal rate of return of the financial asset or liability. Before showing the effective interest rate method of amortization, I want to show some more transactions. In both the discount and premium, the difference between the straight-line and the effective interest amortization methods is not significant.

The table below shows how this example bond would be accounted for over the full 10-year period. Note that the only static figure is the amount of cash interest — interest expense and amortization are different in every single year. Over time, the carrying amount of the bonds is slowly reduced to \$100,000 due to the amortization of the premium each year.

Assume that the final payment will be \$2,774.99 in order to eliminate the potential rounding error of \$1.06. When the first payment is made, part of it is interest and part is principal.

When bonds are sold at a discount or a premium, the interest rate is adjusted from the face rate to an effective rate that is close to the market rate when the bonds were issued. Therefore, bond discounts or premiums have the effect of increasing or decreasing the interest expense on the bonds over their life. Under these conditions,it is necessary to amortize the discount or premium over the life of the bonds by using either the straight-line method or the effective interest method. The effective interest amortization method is more accurate than the straight-line method. International Financial Reporting Standards require the use of the effective-interest method, with no exceptions. 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.

• Although some bonds pay no interest and generate income only at maturity, most offer a set annual rate of return, called the coupon rate.
• The carrying value of the bonds at the beginning of the period by the contractual interest rate.
• If the straight-line method is used to amortize the \$40,000 premium, you would divide the premium of \$40,000 by the number of payments, in this case four, giving a \$10,000 per year amortization of the premium.
• Negative and positive amortizations for a position caused by changes to the position, transfer postings, or key date valuations are posted to offsetting accounts in Financial Accounting.

And the difference between them is the amortization of premium. We will illustrate the problem by the following example related to a premium bond. Learn about the three types of vertical integration strategies and their benefits through examples of how the strategies are used. This lesson is an overview of capital markets, money markets, and examples of the most popular instruments traded in each market. There are different types of bonds which have different characteristics that require different issuing procedures. Learn about secured and unsecured bonds, term and serial bonds, registered and bearer bonds, and convertible and callable bonds. David Ingram has written for multiple publications since 2009, including “The Houston Chronicle” and online at Business.com.

A \$100,000 bond is being paid off in \$5,000 semi-annual payments. On the straight line method, \$4,500 would go to interest each payment like this. As you can see, each payment reduces the bond payable account, but the interest expense stays the same. Thus, the interest expense is becoming a greater portion of bond payable account.

Author: David Ringstrom