Bond Inputs
Advanced note: this calculator solves yield numerically from the bond pricing equation and also reports effective yield, duration, convexity, and price sensitivity.
Example Data Table
This sample shows a typical premium or discount bond setup you can test immediately.
| Bond Label | Market Price | Face Value | Coupon Rate | Years | Payments/Year | Redemption Value | Approx. Solved YTM |
|---|---|---|---|---|---|---|---|
| Sample Corporate Bond | 950.00 | 1000.00 | 6.00% | 8.00 | 2 | 1000.00 | 6.8213% |
| Municipal Bond | 1050.00 | 1000.00 | 4.50% | 12.00 | 2 | 1000.00 | 3.9721% |
Formula Used
The calculator solves the yield that makes present value equal the market price.
Bond Price Equation
Price = Σ [Coupon / (1 + y/m)t] + Redemption Value / (1 + y/m)n
Where y is annual yield, m is payments per year, and n is total coupon periods.
The page solves this equation with an iterative root-finding method, then reports duration, convexity, and scenario-based repricing.
Approximate YTM Check
Approx. YTM ≈ [Annual Coupon + (Redemption Value − Price) / Years] ÷ [(Redemption Value + Price) / 2]
How to Use This Calculator
- Enter the current bond price investors pay today.
- Enter face value, coupon rate, and the redemption value.
- Set years remaining and the coupon payment frequency.
- Use an initial yield guess to help the numerical solver start.
- Choose graph range and graph step for the price sensitivity curve.
- Click Calculate YTM to show results above the form.
- Review solved YTM, effective yield, duration, convexity, and scenario pricing.
- Download the result tables as CSV or PDF for sharing.
Frequently Asked Questions
1) What is yield to maturity?
Yield to maturity is the annualized return earned if a bond is bought at today’s price, coupons are received as scheduled, and the bond is held until final redemption.
2) Is YTM the same as coupon rate?
No. Coupon rate is based on face value only. YTM also reflects market price, time remaining, coupon timing, and any gain or loss when the bond matures.
3) Why can YTM differ from current yield?
Current yield only divides annual coupon income by market price. YTM goes further by including reinvestment assumptions and the maturity price convergence effect.
4) Can this calculator handle zero-coupon bonds?
Yes. Set the coupon rate to zero. The solver will still calculate the return implied by buying below, at, or above redemption value.
5) What does payment frequency change?
Payment frequency changes coupon timing and discounting per period. Semiannual, quarterly, and monthly structures may produce different effective annual results from the same stated coupon rate.
6) Why is redemption value important?
Some bonds redeem at par, while others may repay a different amount. Redemption value directly affects the bond’s final cash flow and solved yield.
7) Is YTM guaranteed?
No. YTM is a model-based estimate. Actual realized return can differ because of default risk, early sale, reinvestment rates, taxes, or changing market conditions.
8) When is approximate YTM useful?
Approximate YTM is useful for quick screening and rough comparisons. The solved YTM from the full pricing equation is more precise for decision-making.