💵 Fixed Income

Bond Pricing Formula & Yield to Maturity (YTM) Calculator

How to calculate bond price and yield to maturity. Bond pricing formula using spot rates and YTM, with step-by-step calculation examples.

Key Concepts

Bond Pricing

PV of future cash flows discounted at YTM. Premium: coupon > YTM. Discount: coupon < YTM. Par: coupon = YTM.

Spot Rates

Yields on zero-coupon bonds. Used to discount each cash flow at the appropriate maturity rate.

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Formulas

From this module

Bond Price (YTM)

P = Σ C/(1+y)t + FV/(1+y)n

Where: y = YTM per period

Bond Price (Spot Rates)

P = C/(1+S1) + C/(1+S2)² + ... + (C+FV)/(1+Sn)n

Where: S<sub>t</sub> = spot rate for maturity t

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Master Formula Sheet -- Fixed Income

Bond Price

P = Σ[C/(1+r)ᵗ] + FV/(1+r)ⁿ

PV of coupons + PV of par

Current Yield

CY = Annual Coupon / Price

Income return only

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Decision Frameworks

When does a bond trade at premium/discount?

Use when:

  • Premium: coupon rate > market yield (investors pay extra for higher coupons)
  • Discount: coupon rate < market yield
  • Par: coupon rate = market yield

Avoid when:

  • Confusing clean and dirty prices when calculating returns

Test Your Understanding

A bond trading at a premium has:

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