Enter bond assumptions
Use the fields below to estimate price, accrued interest, yield-based value, and sensitivity metrics for coupon-paying bonds.
Example data table
| Scenario | Face value | Coupon rate | Yield | Years | Frequency | Indicative clean price |
|---|---|---|---|---|---|---|
| Par bond | 1,000 | 5.00% | 5.00% | 10 | 2 | 1,000.00 |
| Premium bond | 1,000 | 7.00% | 5.50% | 8 | 2 | 1,096.84 |
| Discount bond | 1,000 | 4.25% | 6.50% | 12 | 2 | 824.91 |
| Monthly coupon | 5,000 | 6.20% | 5.90% | 5 | 12 | 5,066.73 |
Formula used
The calculator discounts every remaining coupon and redemption payment back to the settlement date using the market yield per coupon period.
Coupon payment: C = Face Value × Coupon Rate ÷ Payments Per Year
Periodic yield: r = Market Yield ÷ Payments Per Year
Dirty price: Bond Value = Σ [Cash Flowt ÷ (1 + r)t]
Accrued interest: Accrued Interest = Coupon Payment × Elapsed Coupon Fraction
Clean price: Clean Price = Dirty Price − Accrued Interest
Macaulay duration: Duration = Σ(Time × Present Value of Cash Flow) ÷ Dirty Price
Modified duration: Modified Duration = Macaulay Duration ÷ (1 + r)
Convexity: Convexity estimates how duration changes when yield moves and improves price sensitivity analysis for larger interest-rate shifts.
How to use this calculator
- Enter the bond’s face value and annual coupon rate.
- Provide the market yield that investors currently require.
- Add years remaining until maturity and the coupon frequency.
- Enter redemption value if it differs from face value.
- Set the elapsed coupon period percentage for accrued interest.
- Click the calculate button to display price and risk metrics.
- Review clean price, dirty price, duration, convexity, and yield.
- Export the results table to CSV or PDF if needed.
Frequently asked questions
1. What is bond valuation?
Bond valuation estimates a bond’s fair price by discounting future coupon payments and redemption value using the required market yield.
2. Why are clean price and dirty price different?
Dirty price includes accrued interest since the last coupon date. Clean price removes that accrued portion, making quoted prices easier to compare.
3. What happens when yield rises?
Bond prices generally fall when required yield increases because future cash flows are discounted more heavily.
4. What does duration tell me?
Duration measures price sensitivity to yield changes. Higher duration usually means larger price swings when interest rates move.
5. Why is my bond trading at a premium?
A bond trades above redemption value when its coupon rate is higher than the market yield investors currently demand.
6. Can I use this for zero coupon bonds?
Yes. Enter a coupon rate of zero. The calculator will discount only the redemption value back to the settlement date.
7. What is convexity used for?
Convexity improves interest-rate risk analysis by showing how duration changes as yields move. It is useful for larger rate shifts.
8. Does coupon frequency matter?
Yes. Frequency changes coupon size, discount periods, accrued interest timing, and overall present value, especially for longer maturities.