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Finance

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.

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

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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