Bond Price Calculator
Estimate a bond's theoretical clean price by discounting its coupon payments and face value at a given yield.
Input Data
Results
At a glance:Bond price is the present value of a bond's future coupon payments plus its face value at maturity, discounted at the market yield. Formula: price = sum(coupon per period / (1 + r)^t) + face value / (1 + r)^n, where r = annual yield / frequency and n = years x frequency. Example: face value HK$100, coupon 5%, 10 years, annual, at a 4% yield gives about HK$108.18. WARNING: This is the clean price (excluding accrued interest); the actual traded dirty price = clean price + accrued interest. The model assumes a single flat yield and ignores credit risk, call features and reinvestment risk.
Formula
Price = Σ [C / (1 + r)^t] + F / (1 + r)^n.
r = annual yield / frequency, n = years × frequency, C = coupon per period = face value × coupon rate / frequency.
$$P = C \\times \\dfrac{1 - (1 + r)^{-n}}{r} + \\dfrac{F}{(1 + r)^{n}}$$How to Use
- Enter the face value, coupon rate, market yield, years to maturity and coupon frequency.
- View the estimated clean price, coupon per period and total periods.
- To estimate the actual settlement amount, add accrued interest based on the trade date.
FAQ
Is this the clean price or the dirty price?
The calculator gives the clean price — the theoretical price excluding accrued interest, as if on a coupon date. In the market you usually pay the dirty price = clean price + accrued interest, because the seller has accrued part of the next coupon. Accrued interest = coupon per period x days held / days in the coupon period.
Does a higher coupon frequency change the price?
With the same coupon, face value, yield and term, a higher frequency changes the price only slightly, because you receive coupons earlier and can reinvest. The difference is usually small; the dominant driver is the yield relative to the coupon rate.
Are longer bonds more sensitive to rate changes?
Yes. Longer maturities have more of their cash flows (especially the face value) far in the future, so they are more sensitive to yield changes — a 1% rise in yield drops a long bond's price much more than a short bond's. Duration quantifies this sensitivity.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.