# Effective Interest Method of Amortization

## What is the effective interest method of amortization

Under the **effective interest method**, a constant interest rate, equal to the market rate at the time of issue, is used to calculate periodic interest expense. Thus, 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. Furthermore, when the effective interest method is used, the carrying value of the bonds will always be equal to the present value of the future cash outflow at each amortization date.

## Explanation

Although the straight-line method is simple to use, it does not produce the accurate amortization of the discount or premium. It makes the unrealistic assumption that the interest cost for each period is the same, even though the carrying value of the liability is changing. For example, under this method, each period’s dollar interest expense is the same, but as the carrying value of the bond increases or decreases, the actual percentage interest rate correspondingly decreases or increases. For example, the Valenzuela bonds issued at a discount (click to see example) had a carrying value of $92,976 at the date of their issue. The interest expense based on straight-line amortization for the period between January 2, 2020, and July 1, 2020, is $6,702.

This results in an actual percentage interest rate of 7.2%, or $92,976. In the next interest period, this rate falls to 7.15% because the interest expense for the period remains at $6,702, but as shown in Exhibit (bonds issued at a discount), the bond’s carrying value has increased to $93,678. As a result, the percentage interest rate is now 7.15% Or $6,702 / $93,678. Over the life of the bond, this percentage interest rate continues to decrease until January 2, 2025, when it reaches 6.7%, or $6,702 / $99,294.

In the premium example, the same conceptual problem occurs, except that the percentage rate continuously increases as the carrying value of the bond decreases from $107,722 to $100,000, whereas the semiannual interest expense remains constant at $5,228.

Because of the conceptual problem with the straight-line method, the Financial *Accounting* Standards *Board* (FASB) required that the effective interest method be used unless there are no material differences between the two. We will illustrate the effective interest method for both the discount and the premium cases.

## Amortization under Effective Interest Method

### Discount Amortization

As illustrated, the $1007000, 5-year, 12% bonds issued to yield 14% were gold at a price of $92,976, or at a discount

of $7,024, Below Exhibit shows how this discount is amortized using the effective interest method over the life of the bond.

In this exhibit, the effective periodic bond interest expense is calculated by multiplying the bond’s carrying value at the beginning of the period by the semiannual yield rate determined at the time the bond was issued. In this case, the interest expense of $6,508 in Column 2 on July 1, 2020, is equal to $92,976 multiplied by 7%. The difference between the required cash interest payment of $6,000 in Column 3 ($100,000 x 6%) and the effective interest expense of $6,508 is the required discount amortization of $508 in Column 4.

Finally, the unamortized discount of $6,516 on July 1, 2020, in Column 5 is equal to the original discount of $7,024, less the amortized discount of $508. The carrying value of the bond in Column 6 is thus increased by $508, from $92,976 to $93,484. Alternatively, the bonds carrying value on July 1, 2020, is equal to the unamortized discount of $6,516.

The information for the journal entry to record the semiannual interest expense can be drawn directly from the amortization schedule. The entry on July 1, 2020, is:

The following table compares the two different methods of discount amortization for the first three interest periods and for the total overall 10 periods:

Ag the table indicates, under the straight-line method the interest for each period is $6,702i and the total overall 10 periods is $67,024, Under the effective interest method, the semiannual interest expense is $6,508 in the first period and increases thereafter as the carrying value of the bond increases. With the effective interest method, as with the straight-line method, the total interest expense is $67,024. The important point is that there is no difference in the total interest expense but only in the allocation within the 5-year period of time.

### Premium Amortization

As Exhibit ‘A’ in Bonds Issued at a Premium shows, the $100,000, 5-year, 12% bonds issued to yield 10% were issued at a price of $107522, or at a premium of $7,722. The schedule in the below Exhibit shows how the premium is amortized under the effective interest method. This schedule is set up in the same manner as the discount amortization schedule in the above exhibit, except that the premium amortization reduces the cash interest expense every period.

For each period, the interest expense in Column 2 is the semiannual yield rate at the time of issue, 5%, multiplied by the carrying value of the bonds at the beginning of the period. The difference between this amount and the cash interest in Column 3 is the premium amortization in Column 4. The carrying value of the bond at the end of the period in Column 6 is reduced by the premium.amortization for the period.

The journal entry to record the semiannual interest expense can be drawn directly from this schedule. The entry on July 1, 2020, is:

As with the discount example, the total interest expense over the life under the straight-line and the effective interest methods is the same, However, It allocated differently among periods, In both the discount and the premium the difference between the straight-line and the effective interest amortization methods is not significant, but for large bond issues the difference between methods can become significant. If this is the case, accepted accounting principles require that effective interest amortization be used.