Zero-Coupon Bond Yield Calculator
Calculate the Yield to Maturity (YTM) for zero-coupon bonds. Determine implied interest rates and compare deep-discount bonds against standard fixed-income securities.
About
Investors utilize zero-coupon bonds to lock in a specific return over a fixed duration without the reinvestment risk associated with periodic coupon payments. Since these bonds are sold at a discount to their face value, the return is generated entirely by capital appreciation. This tool solves for the Yield to Maturity (YTM), effectively converting the discount depth into an annualized percentage rate. Accuracy in this calculation is critical for comparing the implied interest of a zero-coupon instrument against coupon-bearing bonds or other interest-rate sensitive assets.
Understanding the implied rate allows for better duration management in a fixed-income portfolio. By inputting the face value, purchase price, and time to maturity, investors can determine if a bond's market price reflects a competitive yield relative to the current yield curve. This calculation accounts for the compounding effect over the bond's life, distinguishing between nominal gain and the effective annual growth rate.
Formulas
The Yield to Maturity for a zero-coupon bond is calculated by isolating the rate r in the present value formula. Since there are no periodic coupons, the formula simplifies to a geometric growth equation:
Where F is the Face Value (Par), P is the Purchase Price, and n is the time to maturity in years. If the maturity is given in days, n is calculated as:
Reference Data
| Maturity Period | Face Value $ | Purchase Price $ | Implied Yield (YTM) | Risk Factor |
|---|---|---|---|---|
| 3 Months (T-Bill) | 1,000 | 987.50 | 5.15% | Interest Rate Risk (Low) |
| 6 Months | 1,000 | 975.00 | 5.20% | Interest Rate Risk (Low) |
| 1 Year | 1,000 | 950.00 | 5.26% | Inflation Risk (Med) |
| 5 Years | 5,000 | 3,900.00 | 5.09% | Duration Risk (High) |
| 10 Years | 10,000 | 6,100.00 | 5.06% | Duration Risk (High) |
| 20 Years | 10,000 | 3,700.00 | 5.08% | Volatility (Very High) |
| 30 Years | 20,000 | 4,500.00 | 5.04% | Volatility (Extreme) |
| STRIPS (15Y) | 1,000 | 480.00 | 4.99% | Liquidity Risk (Med) |