Calculator inputs
Enter a quoted bond price and core bond details. The tool converts clean quotes to dirty price when needed, then solves the annual yield to maturity numerically.
Example data table
| Face Value | Coupon Rate | Quoted Price | Accrued Interest | Years | Payments/Year | Redemption | Approx. YTM |
|---|---|---|---|---|---|---|---|
| 1,000 | 5.00% | 980.00 | 0.00 | 5 | 2 | 1,000 | 5.47% |
| 1,000 | 6.00% | 1,045.00 | 0.00 | 7 | 2 | 1,000 | 5.18% |
| 1,000 | 4.50% | 915.00 | 0.00 | 10 | 1 | 1,000 | 5.64% |
| 1,000 | 7.25% | 1,120.00 | 8.00 | 12 | 2 | 1,000 | 5.86% |
| 5,000 | 3.80% | 4,760.00 | 12.50 | 8.5 | 4 | 5,000 | 4.49% |
Formula used
Dirty bond price is solved from discounted future cash flows:
P = Σ [ C / (1 + y/m)^t ] + [ M / (1 + y/m)^N ]
Where P is dirty price, C is coupon per period, y is annual yield, m is payments per year, M is redemption value, and N is total periods.
This calculator starts with the observed bond price and numerically solves for y. It uses a bisection method, which is stable for conventional fixed-rate bonds.
Current yield is calculated as:
Annual Coupon / Quoted Price
Modified duration is calculated from the solved yield and measures approximate price sensitivity to small rate changes.
Convexity adds a second-order view of price movement and helps explain why bond prices do not move in a perfectly straight line.
How to use this calculator
- Enter the bond’s face value and annual coupon rate.
- Choose whether the quoted market price is clean or dirty.
- Add accrued interest when needed, especially for clean-price quotes.
- Enter years remaining to maturity and the coupon payment frequency.
- Set the redemption value, usually the amount repaid at maturity.
- Press Calculate yield to display YTM above the form.
- Review effective yield, current yield, duration, convexity, and cash flows.
- Use the export buttons to save the results as CSV or PDF.
FAQs
1. What does bond price to yield mean?
It means solving the yield that makes the present value of remaining coupons and maturity value equal the bond’s market price today.
2. Why is YTM different from coupon rate?
Coupon rate is based on face value only. YTM also reflects purchase price, time to maturity, coupon timing, and redemption value.
3. What is the difference between clean and dirty price?
Clean price excludes accrued interest. Dirty price includes accrued interest and is the actual cash amount used to solve yield accurately.
4. Does this calculator work for premium bonds?
Yes. It handles premium, discount, and par bonds by discounting all future cash flows and numerically solving the matching annual yield.
5. What does current yield tell me?
Current yield compares annual coupon income with the quoted price. It ignores maturity value and time, so it is not a complete return measure.
6. Why are duration and convexity useful?
Duration estimates price sensitivity to yield changes. Convexity improves that estimate by capturing the bond price curve’s shape.
7. Can I use decimal years to maturity?
Yes. The calculator accepts decimal years and rounds maturity to the nearest payment period for the discounting schedule.
8. Is this suitable for zero-coupon bonds?
Yes. Set coupon rate to zero, keep the redemption value, and the solver will estimate the yield from price and maturity alone.