# How to Calculate an Amortized Bond Premium

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Bonds sell at a value either at a premium, higher than their face value, or at a discount, below their face value. Bonds are sold at a premium because the market's interest rate is lower than the coupon rate. Amortization of a bond decreases the interest expense paid each period. The difference between the bond's carrying value and the bond's face value is the premium or discount of the bond.

## Effective Interest Method

Calculate interest expense by multiplying the net carrying value of the bond by the effective interest rate. The net carrying value is the original amount paid for the bond subtracted by previous amortization. For example, a \$1 million bond sells at a premium for \$1.05 million to yield 10 percent semiannually, due in five years. The bonds coupon rate is 16 percent. Multiply \$1,050,000 by 5 percent, which equals \$52,500.

Calculate interest paid by multiplying the bond's face value by the bond's coupon rate. In the example, it is multiplying \$1,000,000 by 8 percent because the bond's coupon rate is 16 percent semiannually, which equals \$80,000.

Subtract interest expense from the interest paid to determine the amortization. In the example, \$80,000 minus \$52,500 equals \$27,500 of amortized premium in the first year.

## Straight-Line Method

Determine the bond's premium by subtracting the bond's face value by the bond's carrying value. In the example, \$1,050,000 minus \$1,000,000 equals \$50,000.

Determine the number of periods outstanding. In the example, there is five years remaining on the bond, but the bond pays interest semi-annually, so there are 10 periods remaining.

Divide the premium by the number of periods remaining to calculate premium amortization. In the example, \$50,000 divided by 10 periods equals \$5,000 of premium amortization.

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