Bonds can be bought or sold on the open market. When interest rates go down, the value of an existing bond will typically be higher than its original price (the par value) because it pays higher interest than what you can get at present. The unamortized bond premium is the excess of the bond's selling price over its par value. You typically need to calculate the unamortized bond premium because you can write it off against expenses for the remainder of the bond's life, potentially allowing you to save on taxes.

## Calculations

Obtain the interest rate you will use to calculate the present value of the coupons and maturity value. Go to Bloomberg.com, select "Market Date," then "Rates & Bonds," then "US Treasuries." Select the 10-year U.S. Treasury bond yield if you are discounting a bond with 10 or fewer years remaining to maturity. Select the 30-year U.S. Treasury bond yield if you are discounting a bond with 10 to 30 years remaining to maturity.

Convert the bond yield to match the frequency of the coupon payments. Use the formula i = (1+BY)^(1/f)-1, where BY is your bond yield and f is the number of coupons payable per year. This will be your discount factor. If you are using a 30-year bond yield of 3.1 percent and the bond pays semi-annual coupons, your discount factor will be 1.031^(1/2) - 1 = 1.5382 percent.

Calculate the present value of the bond's remaining coupons. Use the formula: C *[1-(1/(1+i)^n)] / i, where C is the amount of each coupon, i is your discount factor and n is the number of coupons remaining. If the bond has 20 years of semi-annual coupons of $25 remaining, then C is $25 and n is 40, and your present value is equal to $25 * [1-(1/1.015382)^40] / 0.015382 = $742.71.

Calculate the present value of the bond's maturity value. Use the formula MV / (1+i)^n, where i is your discount factor and n is the number of coupon payments remaining. If your bond with 40 coupons of $25 remaining has a maturity value of $1,000, then the present value of the maturity value is $1,000 / 1.015382^40 = $543.03.

Add the present value of the remaining coupons and the present value of the maturity value together to get the bond's fair market price. This is the bond's fair market price.

Subtract the bond's original par value from the fair market price to obtain the unamortized bond premium.

### References

### Photo Credits

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- Annual vs. Semi-annual Bond Analysis
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- How to Calculate the Fair Market Price of a Bond Yield to Maturity
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