Zero coupon bond price calculator

This zero coupon bond price calculator allows you to calculate the price of a zero coupon bond based on face value, yield to maturity, and years to maturity. You can enter fractional values into the years to maturity box (such as 9.58 years). By default the calculator assumes that the interest is compounded annually. You can change it to semi-annual compounding through the radio buttons.

As you enter or change values, the calculator automatically updates and displays the bond price.

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What is a bond?

A bond is a fixed-income instrument representing a loan made by an investor to a borrower, typically corporate or governmental. Bonds are used by companies, municipalities, states, and sovereign governments to finance projects and operations. When you buy a bond, you are lending money to the issuer in exchange for periodic interest payments (called coupon payments) and the return of the bond’s face value when it matures.

What is a zero-coupon bond?

A zero-coupon bond is a type of bond that doesn’t pay periodic interest, also known as a coupon. Instead, it’s issued at a deep discount to its face value, and the investor receives the face value of the bond at maturity. The difference between the purchase price and the face value represents the interest income that the investor earns.

Key features of zero-coupon bonds:

1. No periodic interest payments: Unlike traditional bonds that pay interest semi-annually or annually, zero-coupon bonds don’t make any interest payments during their term. The interest is effectively “built into” the bond’s price.
2. Sold at a discount: Zero-coupon bonds are issued at a price significantly lower than their face (par) value. For example, an investor might buy a zero-coupon bond with a face value of $1,000 for $500. When the bond matures, the investor receives the full $1,000.
3. Interest rate densitivity: Zero-coupon bonds are highly sensitive to changes in interest rates. Since they don’t pay periodic interest, their value fluctuates more than that of regular bonds with interest payments when market interest rates change.
4. Tax considerations: In some jurisdictions, even though the bondholder doesn’t receive periodic interest payments, they may still have to pay taxes each year on the “imputed” interest—the difference between the bond’s purchase price and its value at the end of each year.
5. Uses: Investors often use zero-coupon bonds for long-term goals, like saving for retirement or funding a child’s education, because the bonds provide a lump sum payment at a specific future date.

Examples of zero-coupon bonds:

• U.S. Treasury STRIPS: These are government bonds that have been “stripped” of their coupons, meaning that both the principal and the interest portions are sold separately as zero-coupon bonds.
• Municipal and corporate zero-coupon bonds: Some municipalities and corporations also issue zero-coupon bonds, which may be attractive to investors depending on their tax situation and investment goals.

Zero-coupon bonds can be an attractive option for investors looking for a predictable payout at a future date, but they come with risks, particularly interest rate risk, and potential tax implications.

Zero coupon bond price formula

The price of a zero coupon bond is the sum of the present value of its face value at maturity.

P = \frac{F}{(1 + r)^{T}}

• P = Price of the bond
• r = Discount rate or yield
• T = Number of periods
• F = Face value of the bond

The formula above assumes annual compounding. If we assume semi-annual compounding then the formula is

P = \frac{F}{(1 + \frac{r}{2})^{(T\times2)}}

Additional information about bonds

• Credit risk: The risk that the bond issuer may default on its payments. Higher credit risk typically results in higher interest rates.
• Interest rate risk: The risk that the bond’s price will decrease due to rising interest rates. Bond prices and interest rates have an inverse relationship.
• Callable bonds: Some bonds can be “called” (redeemed) by the issuer before their maturity date, usually when interest rates drop. Callable bonds typically offer higher yields to compensate for the risk of being called early.
• Bond ratings: Bonds are rated by credit rating agencies like Moody’s, S&P, and Fitch. Ratings range from AAA (highest quality) to D (default).
• Tax considerations: Interest income from bonds may be subject to federal, state, and local taxes. Municipal bonds, however, often offer tax-free interest.
• Liquidity: Bonds can vary in liquidity. Government bonds tend to be more liquid, while corporate or municipal bonds may be less so.

Bonds are an essential part of many investment portfolios, offering a balance of risk and return, especially for those seeking income stability and capital preservation.