Bond Price Calculator
Enter the bond's face value (par), annual coupon rate, yield to maturity (YTM), years remaining and coupon frequency (annual, semi-annual, quarterly or monthly). The tool applies the discounted-cash-flow formula Price = Σ C/(1+y/m)^k + F/(1+y/m)^N to instantly return the theoretical bond price, the premium or discount versus par, the present value of all coupons, the present value of the face redemption and the current yield (annual coupon ÷ price). Useful for fixed-income analysts, CFA candidates, classroom demos and retail investors comparing entries.
Please enter valid numbers: face value > 0, rates 0–100 %, years 0.25–100.
Theoretical bond price
925.61
Discount (price < face — coupon below YTM)
Premium / discount vs face
−74.39
Current yield (annual coupon ÷ price)
5.40 %
PV of all coupon payments
—
PV of face value at maturity
—
Coupon per period
—
Total periods N
—
Formula
Price = Σ C × (1+y/m)^−k + F × (1+y/m)^−N
Price equals the present value of every future coupon plus the par redemption, each discounted at the per-period yield. When YTM equals the coupon rate the price is exactly par; higher YTM → discount; lower YTM → premium. Real-market quotes layer on credit risk, taxes, liquidity and accrued interest (clean vs dirty price).
Formula
Price = C × (1 − (1+r)^−N) / r + F × (1+r)^−N with C = F × c / m, r = y / m, N = years × m, c = coupon rate, y = YTM, m = coupon payments per year
- · When YTM equals the coupon rate the bond trades exactly at par. YTM above coupon = the bond sells at a discount; YTM below coupon = premium. Intuition: investors only accept a lower coupon if they buy it cheap enough to match the market yield.
- · PV(coupons) is an annuity: C × (1 − (1+r)^−N) / r. PV(face) is a single discount: F × (1+r)^−N. The two together are the theoretical clean price (excluding accrued interest).
- · Coupon frequency drives both the per-period coupon C and the number of periods N. US Treasuries and most corporates pay semi-annually (m = 2); many European sovereigns pay annually (m = 1); MBS pay monthly (m = 12).
- · Current yield = annual coupon ÷ market price. It ignores any capital gain or loss at maturity; only the YTM captures the full return to par.
- · The tool assumes a flat yield curve — a single YTM discounts every cash flow, as in textbooks. Professional valuations use a spot-rate curve and discount each period at the matching rate.
- · Real transaction price = clean price (this tool) + accrued interest since the last coupon. After the ex-coupon date the seller keeps the next coupon and the bond trades clean.
- · Not designed for callable / putable bonds, floating-rate notes, inflation-linked (TIPS), or convertibles — those need option-pricing or scenario analysis on top of plain DCF.
- · References: Bodie, Kane & Marcus, "Investments" (Ch. 14); Fabozzi, "Bond Markets, Analysis and Strategies" (Ch. 2); CFA Institute Level I — Fixed Income curriculum.
Frequently asked
What is the difference between yield to maturity (YTM) and the coupon rate?
The coupon rate is fixed at issue by the issuer — it is the annual coupon as a percentage of face value ($50 / yr on a 5 % × $1,000 bond, always). YTM is the return implied by the current market price: it is the discount rate that, assuming all coupons are reinvested at it and the bond is held to maturity, makes the present value of every cash flow equal today's price. When market rates rise, the YTM of outstanding bonds rises and their prices fall; the reverse holds when rates fall. So coupon rate is stamped on the bond forever, but YTM moves minute-by-minute with the market.
Why is my bond trading at a discount to par?
Most common reason: market rates have risen since the bond was issued. If you bought a 10-year 2 % coupon $1,000 bond in 2021 at par (YTM 2 %), and similar bonds now yield 5 %, new buyers paying full par would only earn 2 %. They will only buy if discounted enough that holding to maturity gives them ~5 % — roughly $760 here. Secondary reasons: a credit downgrade (the market demands a wider spread for the new risk), illiquidity (small issue size, off-the-run Treasury), or tax/regulatory drag (withholding tax on foreign investors). This calculator handles only the pure rate effect — credit spread sits on top.
Why are most US bonds quoted with semi-annual coupons?
US market convention since the 1790s, inherited from British Gilts. Annual coupons would leave too much income lump-sum-bunched on a long bond; monthly coupons add too much admin cost for the issuer. Semi-annual is the compromise — investors get reasonable reinvestment cadence and issuers keep paperwork simple. Be careful when quoting: a "5 % semi-annual" coupon does pay 5 % per year in cash, but compounded the effective annual yield (BEY → EAY) is ≈ 5.0625 %. This calculator takes the YTM and coupon as nominal annual rates and divides by m internally to get the per-period rate r = y / m.
How are zero-coupon bonds priced?
Set the coupon rate to 0. With no periodic interest the formula collapses to Price = F × (1+y/m)^−N — the par value discounted at a single rate. Example: a $1,000 zero, 10-year maturity, YTM 5 % with semi-annual compounding ⇒ price ≈ $610.27. Zero-coupon bonds have the longest duration (≈ time to maturity), so they are textbook examples of interest-rate risk. US Treasury STRIPS, UK Gilt strips and many bank-issued zero-coupon notes use exactly this calculation.
Why does the clean price I get here not match the broker quote exactly?
Two things. (1) Accrued interest: this tool returns the clean price assuming you are at a coupon date. Real settlements use the dirty (invoice) price = clean + interest accrued since the last coupon (under actual/actual or 30/360 day-count conventions), paid by the buyer to the seller at settlement. (2) Market frictions — credit spread, liquidity premium, tax effects (muni tax exemption, withholding tax) — all shift the YTM the market actually demands. To match a real quote, pull the live YTM from Bloomberg / Tradeweb and feed that in.
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