You can purchase U.S. treasury bonds at a discount or premium. If you purchase a bond at auction for more than its par value, the face amount on the bond, you purchase it at a premium. You only receive interest on the par value of the bond. Thus, when you purchase a bond at a premium, the true interest rate you receive on your initial investment is less than the stated interest rate on the bond. The bond's yield to maturity will be less than simply multiplying the stated interest rate by the par value of the bond. If you purchased a bond for a premium, you can calculate the actual yield to maturity.

Multiply the par value of the treasury bond by the yearly interest rate to determine the yearly coupon interest. For example, if the bond has a par value of $1,000 and a 10 percent yearly interest rate, the yearly coupon interest is $100.

Subtract the par value of the bond from the premium you paid for it to determine the total premium. For example, if you paid $1,100 for the $1,000 bond, the total premium is $100.

Determine the annual premium by dividing the total premium by the number of years until the bond matures. If the $1,000 bond matures in 10 years, the annual premium is $10.

Add the bond's premium price to the par value. Divide the sum by two to determine the average price. In the above example, this results in an average price of $1,050.

Add the annual premium to the yearly coupon interest. Divide the average price by the sum to get your actual yield to maturity. In the above examples, the result is 9.45 percent.