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

> **Definition**
>
> Zero-coupon bonds are issued at a deep discount and they repay the par value at maturity. The difference between the purchase price and the par value is the investor's return.

## What Is a Zero-Coupon Bond?

A zero-coupon bond is an investment in debt that doesn't pay interest. It instead trades at a deep discount. The profit is realized at its maturity date when the bond is redeemed for its full face value.

A zero-coupon bond is also known as an accrual bond.

### Key Takeaways

*   A zero-coupon bond doesn't pay interest to the holder.
*   Zero-coupon bonds are purchased at a deep discount to face value but they're repaid at full face value or par at maturity.
*   The difference between the purchase price of a zero-coupon bond and its par value is the investor's return.
*   They can be subject to interest rate risk if investors sell them before maturity.

![Zero-Coupon Bond: 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.](https://www.investopedia.com/thmb/LYmB7P3czf03ad5a_yvLP8emzEw=/1080x0/filters:no_upscale():max_bytes(150000):strip_icc()/zero-couponbond_final_colorupdate-4f856995db3b4293b8a9d308fb2035fd.jpg)

*— Investopedia / Laura Porter*

## The Basics of Zero-Coupon Bonds

Some bonds are issued as zero-coupon instruments. Others are transformed into zero-coupon instruments after a financial institution strips them of their coupons and repackages them as zero-coupon bonds.

They offer payment at face value at maturity so zero-coupon bonds tend to fluctuate in price on the secondary market much more than [coupon bonds](https://www.investopedia.com/terms/c/couponbond.asp).

## What Is a Bond?

A bond is a tool for a company or a government to borrow money. Investors who purchase bonds are effectively acting as lenders to the issuing entity. The investors earn a return in the form of [coupon payments](https://www.investopedia.com/terms/c/coupon.asp) that are made semiannually or annually throughout the life of the bond.

The bondholder is repaid an amount equal to the [face value](https://www.investopedia.com/terms/f/facevalue.asp) of the bond when the [bond matures](https://www.investopedia.com/terms/m/maturitydate.asp). The par or face value of a corporate bond is typically stated as $1,000.

Investors can purchase the bond below its par value if a corporate bond is issued at a discount. An investor who purchases a bond for $920 at a discount will receive $1,000 when it reaches its maturity date. The $80 return plus coupon payments are the investor's earnings for holding the bond.

Not all bonds have coupon payments, however. Those that do not are referred to as zero-coupon bonds.

## How Zero-Coupon Bonds Work

Zero-coupon bonds are issued at a deep discount, and they 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](https://www.investopedia.com/terms/i/imputedinterest.asp). It's an estimated interest rate for the bond and not an established interest rate. A bond with a face value of $20,000 that matures in 20 years with a 5.5% yield may be purchased for roughly $6,855. The investor will receive $20,000 at the end of the 20 years.

The difference between $20,000 and $6,855 is $13,145. This represents the [interest that compounds](https://www.investopedia.com/terms/c/compoundinterest.asp) automatically until the bond matures. Imputed interest is sometimes referred to as "phantom interest."

The imputed interest on the bond is subject to federal [income tax](https://www.investopedia.com/terms/i/incometax.asp). No coupon payments are made on zero-coupon bonds until maturity but 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 like this:

Price = M ÷ (1 + r)

where:

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

An investor would be willing to pay the following if they wanted to make a 6% return on a bond with a $25,000 par value that's due to mature in three years:

> $25,000 / (1 + 0.06) = $20,991.

The bond would be sold to the investor at $20,991 / $25,000 = 84% of the face value if the debtor accepted this offer. The investor gains $25,000 - $20,991 = $4,009 at maturity. This translates to 6% interest per year.

> **Important**
>
> 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. An investor can put up a small amount of money that grows over time with the bond's deep discount.

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.

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

Payment of interest or coupons is the key difference between a zero-coupon and a regular bond.

Regular bonds are also called coupon bonds. They pay interest over the life of the bond and then repay the principal at maturity.

A zero-coupon bond doesn't pay interest but instead trades at a deep discount. This gives investors a profit at maturity when they redeem the bond for its full face value.

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

The primary factor to consider is the imputed interest rate that the investor will earn at maturity. The price of a zero-coupon bond can be calculated using this 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](https://www.investopedia.com/terms/t/treasurybond.asp). It sets a minimum interest rate relative to imputed interest and the original price discount.

## The Bottom Line

Zero-coupon bonds are an alternative to better-known coupon bonds that pay regular interest to their investors. Zero-coupon bonds pay no interest, but they're purchased at a deep discount and repaid at full price.

Most zero-coupon bonds are long-term issues. Ten or more years is common. They're often used to finance a long-range goal such as paying for a child's college education.

One big thing to consider: The owners of zero-coupon bonds pay a "phantom interest" tax on the bonds' earnings through the years they hold them.  

> **Article Sources**
>
> 1.  U.S. Securities and Exchange Commission. "[Zero Coupon Bond](https://www.investor.gov/introduction-investing/investing-basics/glossary/zero-coupon-bond)."
>     
> 2.  U.S. Code. "[26 USC §1274](https://uscode.house.gov/view.xhtml?req=granuleid:USC-prelim-title26-section1274&num=0&edition=prelim)."
>     
> 3.  U.S. Securities and Exchange Commission. "[Topic No. 403, Interest Received](https://www.irs.gov/taxtopics/tc403)."