Enter Bond Details
Example Data Table
| Scenario | Face Value | Price | Coupon Rate | Years | Frequency | Redemption | Insight |
|---|---|---|---|---|---|---|---|
| Discount Bond | $1,000 | $950 | 6.00% | 7 | 2 | $1,000 | Yield usually exceeds coupon rate. |
| Premium Bond | $1,000 | $1,080 | 8.00% | 5 | 2 | $1,000 | Yield usually falls below coupon rate. |
| Par Bond | $1,000 | $1,000 | 5.25% | 10 | 1 | $1,000 | Yield often matches coupon rate. |
Formula Used
Yield to maturity is the discount rate that makes the present value of all future coupon payments and the redemption value equal to the bond's market price.
Bond price equation:
Price = Σ [Coupon / (1 + y / m)t] + [Redemption / (1 + y / m)N]
- y = annual yield to maturity
- m = payments per year
- t = coupon period number
- N = total number of coupon periods
This calculator solves the equation iteratively with Newton-Raphson. If needed, it switches to a bisection fallback for stability.
Duration measures price sensitivity. Modified duration estimates percentage price change for a small yield move, while DV01 estimates dollar change for one basis point.
How to Use This Calculator
- Enter the bond face value and the current market price.
- Add the stated annual coupon rate and years remaining.
- Choose the number of coupon payments each year.
- Enter the redemption value, usually the par value.
- Set an initial yield guess, tolerance, and maximum iterations.
- Press the calculate button to show the result above the form.
- Review YTM, effective annual yield, current yield, and duration.
- Use the chart, schedule table, CSV, and PDF exports for analysis.
Frequently Asked Questions
1) What does yield to maturity mean?
Yield to maturity is the annualized return earned when a bond is bought at the current price and held until maturity, assuming every coupon payment arrives on schedule and can be reinvested at the same yield.
2) Why can YTM differ from the coupon rate?
YTM includes both coupon income and any gain or loss created by buying above or below redemption value. Coupon rate only measures the stated interest payment relative to face value.
3) Why is my bond labeled premium or discount?
A premium bond trades above redemption value, often because its coupon rate is attractive. A discount bond trades below redemption value, usually because market yields are higher than the bond's coupon rate.
4) What does modified duration tell me?
Modified duration estimates how sensitive the bond price is to a small yield change. Higher values mean larger price swings when interest rates move, all else equal.
5) Why does payment frequency matter?
Payment frequency changes both coupon timing and discounting. More frequent coupons slightly affect present values, effective yield, and duration because cash is received sooner and discount periods become shorter.
6) What is DV01?
DV01 is the approximate dollar price change for a one basis point move in yield. It helps investors compare interest-rate risk across bonds with different prices and durations.
7) Why does the calculator use an iterative solver?
For most coupon bonds, the YTM equation cannot be rearranged into a simple direct formula. An iterative solver repeatedly adjusts the yield until the discounted price matches the market price.
8) Can I use this for zero-coupon bonds?
Yes. Enter a coupon rate of zero. The calculator will then estimate yield using only the purchase price, redemption value, maturity length, and payment frequency settings.