# How to Calculate the Unamortized Bond Premium

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If an investment bond is purchased at a premium price, the amount of premium paid can be amortized over the life of the bond as a tax deduction against the interest earned from the bond. The amount amortized each year is based o the yield-to-maturity of the bond when it was purchased and the unamortized premium remaining from the previous year. The amount of premium amortized each year changes as the remaining premium amount declines.

List the original terms of the bond including face amount, price paid, coupon yield, term and yield to maturity. For an example use a bond with the following values: Face amount: \$100,000. Price: \$108,000 -- \$,8,000 of premium. Coupon Yield: 6 percent, \$6,000 annual interest, paid once a year. Term: 10 years. Yield to Maturity: 4.966 percent.

Calculate the premium amortization for the first year by multiplying the price of the bond by the yield to maturity. The subtract the result from the interest earned from the bond for the year. The result is the premium amortization for the year. In the example, \$108,000 times 4.966 percent is \$5,363.28. Subtracting that amount from the interest earnings of \$6,000 gives an amortization amount of \$636.72. The unamortized premium after owning the bond for one year would be \$7,363.28..

Repeat the calculation for each year the bond has been owned, using the most recent premium amount plus the face amount for the initial calculation. For year two, the math would be \$107,363.28 times 4.966 percent equals \$5,331.66. Subtracting this amount from \$6,000 gives an amortization amount of \$668.34. The premium remaining after the second year would be \$6,694.94.

Repeat the calculation for each year you have owned the bond. The premium left will be the unamortized premium up to this point in time.

#### Tips

• Bond premium amortization is based on the interest payment schedule. If you bond pays interest semi-annually -- which is typical -- you must calculate the amortization for each 6 month period, using half values for the interest paid and yield-to-maturity. The amount of premium amortized increases each year, with the remaining balance amount amortized when the bond matures.