Bond Price from Yield Form
Example Data Table
| Bond | Face Value | Coupon Rate (%) | YTM (%) | Years | Frequency | Approx. Clean Price |
|---|---|---|---|---|---|---|
| Treasury Example | 1000 | 4.5 | 4 | 5 | 2 | 1,022.30 |
| Corporate Example | 1000 | 6 | 7.2 | 10 | 2 | 915.62 |
| Municipal Example | 5000 | 5.25 | 4.8 | 12 | 2 | 5,215.84 |
Formula Used
This calculator discounts each future coupon and redemption payment using the yield to maturity. It also adjusts the timing with an elapsed coupon fraction for accrued interest.
Coupon per period:
C = (Face Value × Annual Coupon Rate) ÷ Payments per Year
Periodic yield:
i = YTM ÷ Payments per Year
Dirty price:
Pricedirty = Σ [CFt ÷ (1 + i)(t - f)]
where t is the coupon period, CF is the coupon or final redemption cash flow, and f is the elapsed fraction of the current coupon period.
Accrued interest:
Accrued Interest = Coupon per Period × Elapsed Fraction
Clean price:
Priceclean = Pricedirty − Accrued Interest
Macaulay duration:
Duration = Σ(Time × Present Value of Cash Flow) ÷ Dirty Price
Modified duration:
Modified Duration = Macaulay Duration ÷ (1 + i)
How to Use This Calculator
- Enter the bond label for easy identification.
- Provide face value, coupon rate, and redemption value.
- Enter yield to maturity and years remaining.
- Select annual, semiannual, quarterly, or monthly coupons.
- Add the elapsed fraction for accrued interest handling.
- Set quantity to estimate total purchase cost.
- Choose a yield range and step for the sensitivity chart.
- Press calculate to show results above the form.
- Review prices, duration, convexity, and the full cash flow table.
- Use CSV or PDF buttons to save the output.
Frequently Asked Questions
1. What does bond price from yield mean?
It means finding today’s value of a bond by discounting all remaining coupon payments and the redemption amount using the required yield.
2. Why can bond price move opposite to yield?
When required yield rises, future bond cash flows are discounted more heavily, so present value falls. When yield drops, present value usually rises.
3. What is the difference between clean and dirty price?
Clean price excludes accrued interest. Dirty price includes accrued interest and is usually the actual amount paid at settlement.
4. Why is accrued interest included here?
Bonds often trade between coupon dates. The seller has earned part of the next coupon, so accrued interest adjusts the transaction value fairly.
5. What does duration tell me?
Duration estimates how sensitive a bond’s price is to yield changes. Higher duration usually means greater price movement for the same yield shift.
6. What is convexity in this calculator?
Convexity measures the curvature in the price-yield relationship. It improves price sensitivity estimates when yield changes are larger.
7. Can I use this for zero coupon bonds?
Yes. Set the coupon rate to zero. The calculator will then discount only the final redemption amount.
8. Which payment frequencies are supported?
This version supports annual, semiannual, quarterly, and monthly coupon schedules, which cover many common fixed income structures.