# How to Calculate the Unamortized Bond Premium

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Bond prices move up and down constantly, and it's common for bond investors to face situations where they have to pay more than the face value of a high-interest bond in order to persuade the current owner to sell it. If you pay a premium to a bond's face value, you can amortize that premium over the remaining term of the bond. Doing so requires that you keep track of the unamortized bond premium so that you can make the appropriate calculations for annual amortization. Below, we'll take a closer look at buying bonds at a premium and handling them correctly for tax purposes.

Why would you pay more than face value for a bond?
The main reason bond prices move has to do with interest rates. If a bond is issued at a given rate and then prevailing interest rates in the bond market fall, then the higher-interest bond looks better than it did previously. That in turn pushes its price higher.

The total bond premium is equal to the market value of the bond less the face value. For instance, with a 10-year bond paying 6% interest that has a \$1,000 face value and currently costs \$1,080 in the market, the bond premium is the \$80 difference between the two figures.

In order to figure out how much of your premium you can amortize each year, you have to know the coupon rate of the bond and the yield to maturity based on the price you actually paid. In the 10-year bond example above, the yield to maturity is roughly 5%. That is less than the 6% coupon rate stated because you're paying more than face value for the bond.

To figure out how much you can amortize each year, you take the unamortized bond premium and add it to the face value. Then multiply the result by the yield to maturity, and subtract it from the actual interest paid. For the first year, the unamortized bond premium is \$80, so you would multiply \$1,080 by 5% to get \$54. Subtract that from the \$60 in interest that the bond pays (\$1,000 multiplied by 6%), and you get \$6. For tax purposes, you can reduce your \$60 in taxable interest by this \$6 for a net of \$54.

For the second year, you've already amortized \$6 of your regular bond premium, so the unamortized bond premium is \$80 minus \$6 or \$74. Multiply \$1,074 by 5% to get \$53.70, subtract it from \$60, and you can see that you'll amortize \$6.30 in the second year, leaving you with \$67.70 in unamortized bond premium.