Zero-Coupon Bond Present Value Calculator
A zero-coupon bond pays no periodic interest — you buy it at a deep discount and receive the full face value at maturity. Its fair price today is simply the face value discounted back at your required yield. Enter the three inputs below and get the present value instantly.
Zero-coupon bond price = Face Value ÷ (1 + YTM)^n. Example: a $1,000 bond maturing in 10 years at 8% YTM is worth $463.19 today — a 53.7% discount off face value. The longer the term or the higher the yield, the steeper the discount.
When to use this calculator
- Pricing a zero-coupon Treasury STRIP or savings bond before buying
- Comparing two bonds with different maturities and yields
- Teaching the time-value-of-money concept in finance courses
- Reverse-engineering the implied YTM from a market price
- Fixed-income portfolio valuation and sensitivity analysis
Worked Example: 10-Year Treasury STRIP
- Face Value: $1,000 | YTM: 8% | Years to Maturity: 10
- PV = $1,000 ÷ (1 + 0.08)^10 = $1,000 ÷ 2.1589 = $463.19
- Discount: 53.7% off face value
- You pay $463.19 today and collect $1,000 in 10 years — a gain of $536.81
How it works
2 min readThe Zero-Coupon Bond Formula
A zero-coupon bond makes a single payment — the face value — at maturity. No coupons, no periodic interest. Its price today is:
PV = FV ÷ (1 + r)^n
The deeper the discount from face value, the higher the implied yield. This is why U.S. Treasury STRIPS, Series EE savings bonds, and many corporate zero-coupon bonds trade at steep discounts.
Present Value Table: $1,000 Zero-Coupon Bond
How much you would pay today for a $1,000 face-value zero-coupon bond at different yields and maturities:
| Years | 3% YTM | 5% YTM | 8% YTM | 10% YTM | 12% YTM |
|---|---|---|---|---|---|
| 1 | $970.87 | $952.38 | $925.93 | $909.09 | $892.86 |
| 2 | $942.60 | $907.03 | $857.34 | $826.45 | $797.19 |
| 3 | $915.14 | $863.84 | $793.83 | $751.31 | $711.78 |
| 5 | $862.61 | $783.53 | $680.58 | $620.92 | $567.43 |
| 7 | $813.09 | $710.68 | $583.49 | $513.16 | $452.35 |
| 10 | $744.09 | $613.91 | $463.19 | $385.54 | $321.97 |
| 15 | $641.86 | $481.02 | $315.24 | $239.39 | $182.70 |
| 20 | $553.68 | $376.89 | $214.55 | $148.64 | $103.67 |
| 30 | $411.99 | $231.38 | $99.38 | $57.31 | $33.38 |
Key Relationships
Zero-Coupon vs. Coupon Bond
| Feature | Zero-Coupon | Coupon Bond |
|---|---|---|
| Periodic payments | None | Yes (semi-annual or annual) |
| Price | Deep discount | Near par |
| Reinvestment risk | None | Yes (coupon reinvestment) |
| Duration | = Maturity | < Maturity |
| Tax (U.S.) | Phantom income | Paid on coupons |
U.S. Treasury STRIPS
The most common zero-coupon bonds for individual investors are U.S. Treasury STRIPS (Separate Trading of Registered Interest and Principal of Securities). A 30-year STRIP at 5% YTM trades at about $231 today — you buy it for $231 and receive $1,000 in 30 years.
Note: In the U.S., phantom interest on Treasury zero-coupon bonds is taxable as ordinary income each year even though no cash is received — check with a tax advisor before investing.
Frequently asked questions
What is a zero-coupon bond?
A bond that pays no periodic interest (no coupons). You buy it at a discount and receive the full face value at maturity. The difference between the purchase price and face value is your total return. Examples include U.S. Treasury STRIPS and Series EE savings bonds.
How do I calculate zero-coupon bond present value?
Use the formula: PV = Face Value ÷ (1 + YTM)^n. For example, a $1,000 bond at 8% YTM maturing in 10 years: PV = 1,000 ÷ (1.08)^10 = $463.19. That's the fair price you should pay today.
What is YTM (yield to maturity) for a zero-coupon bond?
YTM is the annualized return you earn if you buy the bond at today's price and hold it to maturity. For zero-coupon bonds, YTM is straightforward: it's the single discount rate that equates the purchase price to the present value of the face value at maturity.
Why do zero-coupon bonds trade at such a large discount?
Because all the return is delivered at maturity. The longer the term and the higher the yield, the larger the discount. A 30-year bond at 10% YTM trades at only 5.7 cents on the dollar — you pay $57.31 for $1,000 at maturity.
Are zero-coupon bonds more sensitive to interest rate changes than coupon bonds?
Yes. Duration equals maturity for a zero-coupon bond, which is the maximum possible for that term. A 1% rise in rates drops a 10-year zero-coupon bond's price by roughly 9%, versus 7–8% for a 10-year coupon bond. This makes them useful for interest-rate hedging but risky if rates spike.
What are U.S. Treasury STRIPS?
STRIPS (Separate Trading of Registered Interest and Principal of Securities) are zero-coupon bonds created by stripping the coupons and principal from a regular Treasury bond. The Treasury guarantees payment at maturity, making them among the safest zero-coupon investments available.
Is phantom interest on zero-coupon bonds taxable in the U.S.?
Yes. Even though no cash is paid until maturity, the IRS requires you to report the accreted (implied) interest each year as ordinary income. This is called 'phantom income.' Holding zero-coupon Treasuries inside a tax-deferred account (IRA, 401k) avoids this problem.
How is zero-coupon bond price different from a regular coupon bond?
A coupon bond's price is the sum of PV of all coupon payments plus the PV of the face value at maturity. A zero-coupon bond has only one cash flow (the face value at maturity), so the formula is simpler: PV = FV ÷ (1 + r)^n.
Can I use this calculator for corporate zero-coupon bonds?
Yes, the math is identical. Use the bond's stated face value, your required yield (or the market YTM), and the years to maturity. Corporate bonds carry credit risk so the YTM is typically higher than comparable Treasuries, which lowers the price.
How do I find the YTM if I know the market price?
Rearrange the formula: YTM = (FV ÷ PV)^(1/n) − 1. For example, if a 10-year $1,000 bond trades at $500: YTM = (1,000 ÷ 500)^(1/10) − 1 = 2^0.1 − 1 ≈ 7.18% per year.