On this page is a zero coupon bond calculator, to calculate the market price or fair value of a zero coupon bond of known time to maturity, par or face value, and interest rate.
Zero Coupon Bond Calculator
Zero Coupon Bond Calculator Inputs
- Bond Face Value/Par Value ($) - The face or par value of the bond – essentially, the value of the bond on its maturity date.
- Annual Interest Rate (%) - The interest rate paid on the zero coupon bond.
- Years to Maturity - The numbers of years until the zero coupon bond's maturity date.
- Months to Maturity - The numbers of months until bond maturity (not this adds to the years value if you enter both fields).
Zero Coupon Bond Calculator Outputs
- Market Price ($): The market price of the bond, or its true value to fit the input criteria.
What is a zero coupon bond?
A zero coupon bond is a bond which doesn't pay any periodic payments. Instead it has only a face value (value at maturity) and a present value (current value). The entire face value of the bond is paid out at maturity.
It is also known as a deep discount bond.
Benefits and Drawbacks of Zero Coupon Bonds
Zero coupon bonds have a duration equal to their time until maturity, unlike bonds which pay coupons.
Duration of a bond is a length of time representing how sensitive a bond is to changes in interest rates. Since zero coupon bonds have an equal duration and maturity, interest rate changes have more effect on zero coupon bonds than regular bonds maturity at the same time. (Whether that's good or bad is up to you!)
Zero coupon bonds are particularly sensitive to interest rates, so they are also sensitive to inflation risks. Inflation both erodes the value of the dollars the bond will eventually pay.
In the United States, you need to impute the interest for some zero coupon bonds to pay taxes in the current year (possibly also for state or local taxes). One tax workaround is to purchase zero coupon bonds in tax-free accounts such as IRAs, or to purchase zero coupon municipal bonds with no tax obligations. Consult your tax advisor for a full breakdown.
What's the zero coupon bond pricing formula?
The zero coupon bond price formula is:
\frac{P}{(1+r)^t}where:
- P: The par or face value of the zero coupon bond
- r: The interest rate of the bond
- t: The time to maturity of the bond
Zero Coupon Bond Pricing Example
Let's walk through an example zero coupon bond pricing calculation for the default inputs in the tool.
- Face value: $1000
- Interest Rate: 10%
- Time to Maturity: 10 Years, 0 Months
Substituting into the formula:
\frac{P}{(1+r)^t} = \\~\\ \frac{1000}{(1+.1)^{10}} = \\~\\ \frac{1000}{2.5937424601} = \\~\\ \$385.54So a 10 year zero coupon bond paying 10% interest with a $1000 face value would cost you $385.54 today.
In the opposite direction, you can compute the yield to maturity of a zero coupon bond with a regular YTM calculator.
Other Financial Basics Calculators
Zero coupon bonds are yet another interesting security in the fixed income world. For other bond calculators, check out the following:
