Bond Price — Smart Financial Analysis
The foundation of fixed income — every bond's price is the present value of its future cash flows. Calculate premium, par, or discount. Visualize the price-yield seesaw.
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Bonds are priced as the present value of all future cash flows: coupon payments plus face value at maturity. Bond Price = Σ(Coupon / (1+y)^t) + Face / (1+y)^n, where y = yield per period, t = period number, n = total periods. Premium: coupon > yield, price > face value — you pay more for above-market income. Coupon rate is fixed at issuance — it's the annual interest as % of face value.
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Why: Bonds are priced as the present value of all future cash flows: coupon payments plus face value at maturity. Each cash flow is discounted at the yield-to-maturity rate. Bond Pri...
How: Enter Face Value ($), Coupon Rate (%), YTM (%) to get instant results. Try the preset examples to see how different scenarios affect the outcome, then adjust to match your situation.
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Bond Price Calculator — The Foundation of Fixed Income
Every bond's price is the present value of its future cash flows. Premium, par, or discount — visualize the price-yield seesaw.
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Inputs
📉 Bond Price vs Yield Curve (Inverse)
🥧 Price Breakdown (PV of Coupons vs PV of Face)
📊 Price by Maturity at Different Yields
📈 Premium/Discount Spectrum
For educational purposes only — not financial advice. Consult a qualified advisor before making decisions.
💡 Money Facts
Bond Price analysis is used by millions of people worldwide to make better financial decisions.
— Industry Data
Financial literacy can increase household wealth by up to 25% over a lifetime.
— NBER Research
The average American makes 35,000 financial decisions per year—many can be optimized with calculators.
— Cornell University
Globally, only 33% of adults are financially literate, making tools like this essential.
— S&P Global
Bond Price = Σ(Coupon / (1+y)^t) + Face / (1+y)^n — the present value of all future cash flows. The #1 rule: bond prices move INVERSELY to interest rates. When rates rise, existing bond prices FALL (and vice versa). A 10yr bond with 4% coupon swings $163 when yields move from 3% to 5%. The $51 TRILLION US bond market constantly reprices as rate expectations shift. Three pricing states: Premium (coupon > yield, price > face), Par (coupon = yield, price = face), Discount (coupon < yield, price < face). Zero coupon bonds are the most sensitive to rate changes.
📈 By the Numbers
📊 Premium, Par, or Discount?
- Premium (price > par): Coupon rate > YTM. You pay more upfront for above-market income.
- Par (price = par): Coupon rate = YTM. Fair value.
- Discount (price < par): Coupon rate < YTM. You pay less; capital gain at maturity compensates.
📐 Bond Pricing Formula
Bond Price = Σ [Coupon / (1 + r)^t] + Face Value / (1 + r)^n. Where r = YTM per period, n = total periods. This is the sum of the present values of all future cash flows. For semi-annual bonds, divide coupon and yield by 2 and double the number of periods.
💵 Clean vs Dirty Price
Clean price = quoted price (PV of future cash flows). Dirty price = clean price + accrued interest. When you buy between coupon dates, you pay the seller their share of the next coupon.
📉 Rate Sensitivity
Longer maturity and lower coupon = MORE price sensitivity to rate changes. A 30-year zero-coupon bond can swing 20%+ when rates move 1%. A 2-year high-coupon bond might move only 2%. Duration quantifies this sensitivity.
📈 Coupon Rate vs Yield
Current yield = annual coupon ÷ price. It ignores capital gain/loss at maturity. YTM accounts for all cash flows. For premium bonds, current yield overstates return; for discount bonds, it understates it.
🎯 Zero-Coupon Bonds
Zero-coupon bonds pay no interest; they are sold at a deep discount and mature at par. Price = Face Value / (1 + r)^n. They have the highest duration and thus the most rate sensitivity.
📚 Sources
- • SIFMA
- • Treasury Direct
- • CFA Institute
- • Bloomberg
❓ Frequently Asked Questions
How are bonds priced?
Bonds are priced as the present value of all future cash flows: coupon payments plus face value at maturity. Each cash flow is discounted at the yield-to-maturity rate. Bond Price = Σ(Coupon / (1+y)^t) + Face / (1+y)^n. The #1 rule: bond prices move INVERSELY to interest rates.
What is the bond pricing formula?
Bond Price = Σ(Coupon / (1+y)^t) + Face / (1+y)^n, where y = yield per period, t = period number, n = total periods. For semi-annual bonds, divide coupon and yield by 2 and double the number of periods. This is the sum of PV of coupons plus PV of face value.
What is bond premium vs discount?
Premium: coupon > yield, price > face value — you pay more for above-market income. Par: coupon = yield, price = face value — fair value. Discount: coupon < yield, price < face value — you pay less; capital gain at maturity compensates for lower coupons.
What is coupon rate vs yield?
Coupon rate is fixed at issuance — it's the annual interest as % of face value. Yield (YTM) is the market rate that equates price to cash flows. When coupon > yield, bond trades at premium; when coupon < yield, at discount. Current yield = annual coupon / price (ignores capital gain/loss).
How do bond price and interest rates relate?
Bond prices move INVERSELY to interest rates. When rates rise, existing bond prices fall (and vice versa). A 10yr bond with 4% coupon swings ~$163 when yields move from 3% to 5%. Longer maturity and lower coupon = more sensitivity. The $51 trillion US bond market constantly reprices as rate expectations shift.
What is clean vs dirty bond price?
Clean price is the quoted bond price excluding accrued interest. Dirty price (settlement price) = clean price + accrued interest. You pay the dirty price when you buy; the seller receives accrued interest for the period they held the bond. Between coupon dates, accrued interest accrues linearly.
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