# Formula for Amortizing Bonds

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Bonds are often bought and sold after issuance for more or less than their face value. A bond has a fixed interest rate and pays interest at regular intervals until the maturity date of the bond. Market interest rates, in the meantime, fluctuate, making the bond more or less desirable compared to newly-issued bonds. Generally accepted accounting practices (GAAP) require that the premium paid or discount received on the bond be amortized into income over the life of the bond.

## How Bonds Work

When you purchase a bond directly from the corporation or entity selling it, you will buy it for its face value or close to it because it will be issued at a market interest rate. For example, if a corporate issues a \$1,000 bond that pays 7 percent interest and the market rate is also 7 percent, you will pay \$1,000 for that bond. You will receive periodic interest payments at 7 percent per year and, at maturity, you will receive your \$1,000 back. If, instead, you purchase that bond on the open market two years later and the current market rates are 5.5 percent, you would be willing to pay more than \$1,000 for the bond because it pays more than market rates. If you purchase the bond for \$1,150, the extra \$150 is called the bond premium. GAAP requires that you amortize that premium over the life of the bond to maturity to normalize the interest. At the maturity date, all of the premium will be amortized and the recorded bond value will be \$1,000, which is what you will receive when you cash the bond. The same principle works in reverse if market rates are higher than the bond rate. You will pay less than \$1,000 for the bond and will amortize the discount over the life of the bond.

## Recording The Initial Bond Purchase

When you record the initial purchase of the bond, you will debit the investment account on the balance sheet and credit cash. Some companies record the entire amount of the purchase in one balance sheet account, while other keep the discount or premium in a contra account -- a second account beside the investment account. That way, only the face value of bonds held are in the investment account and the contra account shows the amount of premium or discount left to be amortized. Companies with large investment portfolios often do the latter so that they can tell at a glance what they will receive on the maturity of bonds.

## Straight-Line Method

The easiest method of amortizing bonds is straight-line, meaning dividing the discount or premium by the number of years left to maturity and taking that amount onto the income statement every year. For example, if our bond premium is \$150 and we have 11 years left to maturity, the straight-line method will result in an interest expense on the income statement of \$13.64 per year. At a 7 percent posted rate, we will also receive interest income of \$70 per year. The net of the two represents the market interest rate at the time of the purchase. GAAP allows the straight-line method to be used when it would not produce a substantially different result than the effective interest method, otherwise, the latter must be used.

## Effective Interest Method

The effective interest method produces a more accurate result than the straight-line method. This method shows keeps the interest rate constant while the value of the bond moves closer to its face value over time. The amount of interest in each period changes in response to the new amortized bond value. To calculate amortization using the effective interest method, in the first year, multiply the total bond amount recorded by the market interest rate. In our ongoing example, we would multiply \$1,150 by 5.5 percent to equal \$63.25. This is ultimately the amount we want on the income statement. We will be recording the interest payment of \$70, so we amortize the difference by crediting the investment account by \$6.75 and debiting interest expense. The next year we multiply the new amortized bond value of \$1,143.25 by 5.5 percent and make similar adjustments. The total amount of amortization rises over the life of the bond, but the interest rate versus the recorded bond value stays the same.