# Zero-Coupon Bond Definition, Formula, and Example

Zero coupon bonds are long-term fixed income securities. The bonds are sold at a deep discount that makes them attractive for investors looking for a low-cost investment. Zero coupon bonds have maturity dates ranging from one to 40 years with a locked-in interest rate. You can trade zero coupon bonds through your broker or buy and sell them on the major exchanges. Zero coupon bonds are rated by credit rating firms, including Moody’s, Standard & Poor’s and Fitch.

## Definition of a Zero Coupon Bond

Zero coupon bonds are sold at a deep discount compared to their face value. For example, a bond with a face value of \$20,000 could be sold for approximately \$7,000. Although the interest compounds semiannually or annually, you do not receive interest payments over the life of the bond. Instead, you’ll receive the bond’s face value and the cumulative interest in one lump sum when the bond matures. Bond holders may have to pay federal, state or local taxes annually on the unpaid interest amount.

## Formula for Calculating a Zero Coupon Bond Price

You can use a formula to calculate the purchase price of a zero coupon bond. The formula requires that you use a calculator with the scientific notation feature. The formula to calculate the purchase price is F / (1 + r)^t, where "F" stands for the bond’s face value, "r" stands for the interest rate and "t" stands for the maturity time. The "^" is the scientific notation symbol for the power sign. For example, a zero coupon bond has a \$10,000 face value, earns 8 percent interest annually and matures in 10 years. Using the formula, your purchase price is \$10,000 / (1 + .08)^10 = \$10,000 / 2.1589, or \$4,631.99.

## Types of Zero Coupon Bonds

You can choose from several types of zero coupon bonds. Corporate zero coupon bonds usually pay a high interest rate, but the interest is generally taxed at the federal level. Municipal zero coupon bonds pay lower interest but are usually exempt from federal taxation. Strips are derivatives of zero coupon bonds. A brokerage firm buys zero coupon bonds and strips the principal from the interest. The firm then sells either the principal or the interest as a zero certificate. You can buy U.S. Treasury strips that pay either principal or interest.

## Zero Coupon Bond Investing Risks

Zero coupon bonds don’t pay interest until maturity which makes them especially susceptible to interest rate swings. You’ll incur a capital gain or loss if you sell your bond before maturity. They also come with a high risk of default if they are rated as noninvestment grade by the three credit rating agencies. Finally, many federal and state municipalities sell zero coupon bonds that can be called in, or retired, before maturity. If this happens, you’ll lose the interest you would have earned had the bond reached maturity.

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