# Zero-Coupon Bond: Definition, How It Works, and How To Calculate

## What Is a Zero-Coupon Bond?

A zero-coupon bond, also known as an accrual bond, is a debt security that does not pay interest but instead trades at a deep discount, rendering a profit at maturity, when the bond is redeemed for its full face value.

### Key Takeaways

• A zero-coupon bond is a debt security instrument that does not pay interest.
• Zero-coupon bonds trade at deep discounts, offering full face value (par) profits at maturity.
• The difference between the purchase price of a zero-coupon bond and the par value indicates the investor's return.
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## Understanding Zero-Coupon Bonds

Some bonds are issued as zero-coupon instruments from the start, while other bonds transform into zero-coupon instruments after a financial institution strips them of their coupons, and repackages them as zero-coupon bonds. Because they offer the entire payment at maturity, zero-coupon bonds tend to fluctuate in price, much more so than coupon bonds.

A bond is a portal through which a corporate or governmental body raises capital. When bonds are issued, investors purchase those bonds, effectively acting as lenders to the issuing entity. The investors earn a return in the form of coupon payments, which are made semiannually or annually, throughout the life of the bond.

When the bond matures, the bondholder is repaid an amount equal to the face value of the bond. The par or face value of a corporate bond is typically stated as $1,000. If a corporate bond is issued at a discount, this means investors can purchase the bond below its par value. For example, an investor who purchases a bond for$920 at a discount will receive $1,000. The$80 return, plus coupon payments received on the bond, is the investor's earnings or return for holding the bond.

But not all bonds have coupon payments. Those that do not are referred to as zero-coupon bonds. These bonds are issued at a deep discount and repay the par value, at maturity. The difference between the purchase price and the par value represents the investor's return. The payment received by the investor is equal to the principal invested plus the interest earned, compounded semiannually, at a stated yield.

The interest earned on a zero-coupon bond is an imputed interest, meaning that it is an estimated interest rate for the bond and not an established interest rate. For example, a bond with a face amount of $20,000, that matures in 20 years, with a 5.5% yield, may be purchased for roughly$6,855. At the end of the 20 years, the investor will receive $20,000. The difference between$20,000 and $6,855 (or$13,145) represents the interest that compounds automatically until the bond matures. Imputed interest is sometimes referred to as "phantom interest."

The imputed interest on the bond is subject to income tax, according to the Internal Revenue Service (IRS). Therefore, although no coupon payments are made on zero-coupon bonds until maturity, investors may still have to pay federal, state, and local income taxes on the imputed interest that accrues each year. Purchasing a municipal zero-coupon bond, buying zero-coupon bonds in a tax-exempt account, or purchasing a corporate zero-coupon bond that has tax-exempt status are a few ways to avoid paying income taxes on these securities.

## Pricing a Zero-Coupon Bond

The price of a zero-coupon bond can be calculated as:

Price = M ÷ (1 + r)n

where:

• M = Maturity value or face value of the bond
• r = required rate of interest
• n = number of years until maturity

If an investor wishes to make a 6% return on a bond, with $25,000 par value, that is due to mature in three years, they will be willing to pay the following:$25,000 / (1 + 0.06)3 = $20,991. If the debtor accepts this offer, the bond will be sold to the investor at$20,991 / $25,000 = 84% of the face value. Upon maturity, the investor gains$25,000 - $20,991 =$4,009, which translates to 6% interest per year.

The greater the length of time until the bond matures, the less the investor pays for it, and vice versa. The maturity dates on zero-coupon bonds are usually long-term, with initial maturities of at least 10 years. These long-term maturity dates let investors plan for long-range goals, such as saving for a child’s college education. With the bond's deep discount, an investor can put up a small amount of money that can grow over time.

Zero-coupon bonds can be issued from a variety of sources, including the U.S. Treasury, state and local government entities, and corporations. Most zero-coupon bonds trade on the major exchanges.

### Risk in Bonds

Zero-coupon bonds are like other bonds, in that they do carry various types of risk, because they are subject to interest rate risk if investors sell them before maturity.

## How Does a Zero-Coupon Bond Differ From a Regular Bond?

Payment of interest, or coupons, is the key differentiator between a zero-coupon and regular bond. Regular bonds, which are also called coupon bonds, pay interest over the life of the bond and also repay the principal at maturity. A zero-coupon bond does not pay interest but instead trades at a deep discount, giving the investor a profit at maturity when they redeem the bond for its full face value.

## How Does an Investor Price a Zero-Coupon Bond?

An investor chooses the zero-coupon bond they would like to purchase based on several criteria, but one of the main ones will be the imputed interest rate that they can earn at maturity. The price of a zero-coupon bond can be calculated with the following equation:

Zero-coupon bond price = Maturity value ÷ (1 + required interest rate)^number years to maturity

## How Does the IRS Tax Zero-Coupon Bonds?

Imputed interest, sometimes referred to as "phantom interest," is an estimated interest rate. The imputed interest on the bond is subject to income tax. The IRS uses an accretive method when calculating the imputed interest on Treasury bonds and has applicable federal rates that set a minimum interest rate in relation to imputed interest and original issue discount rules.

Article Sources
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1. U.S. Securities and Exchange Commission. "Zero Coupon Bond."

2. U.S. Code. "26 USC §1274."

3. U.S. Securities and Exchange Commission. "Topic No. 403 Interest Received."

4. U.S. Securities and Exchange Commission. "Interest Rate Risk: When Interest Rates Go Up, the Prices of Fixed-rate Bonds Fall."

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