# How to Calculate Interest Expense on a Bond Using YTM i Jupiterimages/Photos.com/Getty Images

When you own a bond, the bond’s issuer typically pays you fixed interest at regular intervals and repays the bond’s face value when it matures. Each interest payment is an expense from the issuer’s perspective and income from yours. To figure the amount of interest a bond pays, you can use its yield to maturity, or YTM, and some of its other basic information. YTM is the rate of return you earn if you hold a bond until it matures. This yield reflects the market interest rate that investors currently demand from the bond.

## Step 1

Find out a bond’s YTM, market price, face value, interest payment frequency and number of years until maturity from your broker or from the bonds page in the market data section of the Financial Industry Regulatory Authority’s website.

## Step 2

Use the equation P = C[(1 - ((1 + (Y/N))^(-N x T)))/(Y/N)] + [F/((1 + (Y/N))^(N x T))], in which P represents price, C is the interest payment for which you’ll solve, Y represents YTM as a decimal, N is the number of payments per year, T is the years until maturity and F is the face value. For example, assume a bond with a \$1,000 face value sells for \$1,100, has a 6 percent YTM, pays semiannual interest and has 15 years until maturity. The equation is \$1,100 = C[(1 - ((1 + (0.06/2))^(-2 x 15)))/(0.06/2)] + [\$1,000/((1 + (0.06/2))^(2 x 15))].

## Step 3

Calculate the second set of brackets. In this example, divide 0.06 by 2 and add 1 to your result to get 1.03. Multiply 2 by 15 to get 30. Raise 1.03 to the 30th power to get 2.4273. Divide \$1,000 by 2.4273 to get \$411.98. This leaves \$1,100 = C[(1 - ((1 + (0.06/2))^(-2 x 15)))/(0.06/2)] + \$411.98.

## Step 4

Solve the numbers in the remaining brackets. In this example, divide 0.06 by 2 to get 0.03. Multiply -2 by 15 to get -30. Add 1 to 0.03 and raise the result to the -30th power to get 0.412. Subtract 0.412 from 1 to get 0.588. Divide 0.588 by 0.03 to get 19.6. This leaves \$1,100 = C(19.6) + \$411.98.

## Step 5

Subtract the number on the right side of the equation from the bond’s price on the left side. In this example, subtract \$411.98 from \$1,100 to get \$688.02, which leaves \$688.02 = C(19.6).

## Step 6

Divide the left side of the equation by the number on the right side to solve for C to determine the bond’s periodic interest payment. In this example, divide \$688.02 by 19.6 to get \$35.10. This means the bond pays interest of \$35.10 every six months.

## Step 7

Multiply your result by the number of payments per year to determine the bond’s total annual interest. Concluding the example, multiply \$35.10 by 2 to get \$70.20 in annual interest.