How the Zero-Coupon Bond Calculator Works
A zero-coupon bond pays no periodic interest — instead, it’s purchased at a discount and matures at full face value. The investor’s entire return comes from that price appreciation.
This zero-coupon bond calculator computes:
- Bond Price — the fair value given a target yield
- Implied Yield to Maturity — the return given a purchase price
- Total Gain at Maturity — the dollar difference between price and face value
- Total Return (%) — the overall percentage gain
Zero-Coupon Bond Formula
Price (given yield)
Price = Face Value ÷ (1 + y/n)^(n×t)
Yield (given price)
y = n × [(Face Value ÷ Price)^(1 ÷ (n×t)) − 1]
Where: - y = Yield to maturity (as a decimal) - n = Compounding periods per year - t = Years to maturity
Zero-Coupon Bond Examples
Example 1: Solving for Price
| Variable | Value |
|---|---|
| Face Value | $1,000 |
| Yield to Maturity | 5% |
| Compounding | Annually |
| Years to Maturity | 10 |
| Bond Price | $613.91 |
Example 2: Solving for Yield
| Variable | Value |
|---|---|
| Face Value | $1,000 |
| Purchase Price | $700 |
| Compounding | Annually |
| Years to Maturity | 10 |
| Implied Yield | 3.63% |
Who Benefits from the Zero-Coupon Bond Calculator?
This zero-coupon bond calculator is designed for:
- Investors evaluating discount bonds like STRIPS or savings bonds
- Parents planning education savings with zero-coupon bonds
- Financial planners matching bond maturities to future liabilities
- Students learning fixed-income pricing concepts
Zero Coupon Bond Calculator Frequently Asked Questions
What is a zero-coupon bond?
A zero-coupon bond is a bond that pays no periodic interest. Instead, it’s sold at a discount to its face value and pays the full face value at maturity, with the difference representing the investor’s return.
How do you calculate the price of a zero-coupon bond?
The price of a zero-coupon bond is calculated by discounting the face value back to the present using the yield to maturity: Price = Face Value ÷ (1 + y/n)^(n×t).
How do you find the yield of a zero-coupon bond?
The implied yield of a zero-coupon bond is found using the purchase price, face value, and time to maturity by rearranging the price formula: y = n × [(Face Value ÷ Price)^(1 ÷ (n×t)) − 1].
Why do zero-coupon bonds trade at a discount?
Since zero-coupon bonds pay no periodic interest, investors buy them below face value so that the price appreciation to face value at maturity represents their entire return.