Transparent method
The formula
Worked example
Example inputs
How to interpret the result
A zero-coupon bond pays no periodic interest at all. Its entire return comes from buying at a deep discount and receiving full face value at maturity, and the difference between those two numbers accrues as imputed interest along the way even though no cash actually changes hands until maturity.
Before you rely on it
What to check
Confirm how imputed interest on a zero-coupon bond gets taxed in your situation, since tax can be owed annually on income that isn't actually received until the bond matures.
The common error
Where people go wrong with zero-coupon bond calculator
Assuming a zero-coupon bond produces no taxable income until maturity because no cash is received until then. In a taxable account, the imputed interest is often taxed annually as it accrues, well before the bond actually pays out.
Sensitivity evidence
How annual yield changes the estimated purchase price
| Annual yield | Estimated purchase price | Accretion to maturity | Price as share of face value |
|---|---|---|---|
| 3.0% | $742 | $258 | 74.2% |
| 4.0% | $673 | $327 | 67.3% |
| 5.0%worked example | $610 | $390 | 61.0% |
| 6.0% | $554 | $446 | 55.4% |
| 7.0% | $503 | $497 | 50.3% |
Every input, tested
Which input moves the estimated purchase price most
| Input | Tested from | To | Estimated purchase price at each end | Swing |
|---|---|---|---|---|
| Years to maturity | 7.0 years | 13.0 years | $708 to $526 | $181 (30%) |
| Face value | $900 | $1,100 | $549 to $671 | $122 (20%) |
| Annual yield | 4.0% | 6.0% | $673 to $554 | $119 (20%) |
| Compounding periods per year | 1 | 3 | $614 to $609 | $4.88 (0.8%) |
Two variables at once
Estimated purchase price by annual yield and face value
| Annual yield \ Face value | $800 | $1,000 | $1,200 |
|---|---|---|---|
| 3.0% | $594 | $742 | $891 |
| 4.0% | $538 | $673 | $808 |
| 5.0% | $488 | $610 | $732 |
| 6.0% | $443 | $554 | $664 |
| 7.0% | $402 | $503 | $603 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Face value | $1,000 |
| Annual yield | 5.0% |
| Years to maturity | 10.0 years |
| Compounding periods per year | 2 |
| Estimated purchase price | $610 |
| Accretion to maturity | $390 |
| Price as share of face value | 61.0% |
Where the inputs come from
Face value is the amount paid at maturity, annual yield is the market's required return, years to maturity is the time until payment, and compounding periods per year follows the bond's convention, two for most US bonds. A zero-coupon bond pays no interest along the way, so its price is the face value discounted at the yield. Treasury STRIPS and corporate zeros are examples, and their yields are on brokerage screens.
Using the estimated purchase price in a real decision
Zero-coupon bonds have known outcomes if held to maturity, which suits a fixed future goal such as a tuition bill, but their prices swing more than coupon bonds when rates change because all the cash arrives at the end.
When the result stops applying
In a taxable account, you owe tax each year on the imputed interest even though you receive no cash, which is called phantom income, so zeros are best in tax-deferred accounts or when the interest is tax exempt. Long-dated zeros are very sensitive to rates. Credit risk applies to corporate zeros. Selling before maturity may give a gain or a loss.
What to compare it with
See the rate sensitivity on the bond duration and convexity calculators, and the yield on the yield to maturity page. The bond ladder and present value calculators help plan future payments, and the TIPS calculator covers inflation-protected bonds. Zeros are useful to match a known future liability.
People also ask
Frequently asked questions
What is phantom income?
Tax owed each year on the interest that accrues on a zero-coupon bond, even though you receive no payment until maturity.
Why are zero-coupon bond prices so volatile?
Because all the value arrives at maturity, so their duration equals their maturity, and a small yield move changes the price by a larger amount than for coupon bonds.
Who uses zero-coupon bonds?
Investors with a known future liability, such as a tuition bill, and those in tax-deferred accounts who want a fixed, predictable payoff.