Zero-Coupon Bond Calculator

What a zero-coupon bond is

A zero-coupon bond makes no interest payments along the way. You buy it for less than its face value and receive the full face value at maturity, and the gap between the two is your entire return. With only one cash flow at the end, it is a pure example of the time value of money.

From the face value, the yield you require, and the time to maturity, the calculator returns the fair price today and the total gain from holding to the end. The mathematics of discounting is the same everywhere, so it works for any market and currency.

How the calculator works

The yield to maturity you enter is converted into a rate per compounding period and the years into a number of periods. The face value is then divided by one plus that rate, raised to the number of periods:

Price = Face value ÷ (1 + y)^n

Here y is the yield per period and n is the number of periods. With annual compounding one year is one period; with semi-annual compounding one year is two periods and the yield is halved for each. The total gain is the face value minus the price you pay today. The price reflects exactly the yield you type, with no stored market assumptions.

Why the discount matters

Suppose a bond will pay 1,000 units of currency in ten years and the market demands a 5% annual yield. Discounting that 1,000 over ten years gives a fair price of about 614. You pay 614 today and, if you hold to maturity, receive 1,000; the 386 difference is your compounded return, earned through the passage of time instead of periodic coupons.

Because the whole payoff is a single future amount, the price is highly sensitive to the yield. A higher required yield discounts the face value more heavily and lowers the price; a lower yield raises it. With no intermediate coupons to soften the effect, zero-coupon bonds have the longest duration of any bond with the same maturity, so their prices swing more when interest rates move.

Compounding frequency

Semi-annual compounding applies the discount twice a year, which produces a marginally lower price for the same stated annual yield. The difference is small but matters when you compare a quoted market price with a fair value, so match the convention used in your market.

Common uses

• Pricing discount securities. Treasury strips, zero-coupon government bonds and discount notes trade on this formula.
• Checking value against the market. If a bond trades at a different price from the one the calculator returns at your target yield, you can see whether it is cheap or expensive relative to your view.
• Planning a future lump sum. If you need a fixed amount on a specific date, such as a tuition bill, a balloon payment, or a maturing obligation, a zero-coupon bond lets you lock it in today at a known cost.

A worked example

With a face value of 1,000, a yield to maturity of 5%, ten years to run, and annual compounding, the price is 613.91 and the total gain 386.09. Switch to semi-annual compounding and the price edges down to about 610. Raise the yield to 7% and the price falls further.

Reading the results

The bond price today is what you would pay to earn your target yield. The total gain is the compounded profit at maturity, and the face value received is what you collect at the end. The donut chart splits the face value into the part you pay upfront and the part that is gain.

Risk and tax

A zero-coupon bond carries its issuer's credit risk: if the issuer defaults, the face value may not arrive. Government-issued zeros have very low credit risk, while corporate zeros carry more. Selling before maturity brings price risk, magnified by the long duration. Many tax systems also treat the yearly growth of the discount as taxable income even though no cash is paid until maturity, so check the treatment in your own country.

About This Zero-Coupon Bond Calculator

Use this zero-coupon bond calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.