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Formula for Calculating the Price of a Coupon Bond formula

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Tags:  bonds pricing and analysis

 Description of the Formula for Calculating the Price of a Coupon Bond formula

The formula below allows the calculation of the price including accrued interest (also referred to as "gross price" or "dirty price") of a coupon bond.

The formula for calculating the value of a coupon bond is based on the concept of present value, which discounts the future cash flows associated with the bond to their current value. The formula takes into account the periodic coupon payments and the final principal repayment at maturity.

  Formula

\[ P_{gross} = \sum_{n=1}^{N} \frac{cpn_{n}}{(1+i)^{t_{n}}}+ \frac{C_{N}}{(1+i)^{t_{N}}} \ \]

 Symbols

\(C_{N}\ \)       
Principal of the bond
\(cpn_{n}\ \)       
Nominal coupon of period n
\(i\ \)       
Yield
\(t_{n}\ \)       
Time between calculation date and the maturity of cash flow n (full years and year fraction)

  Additional information related to this formula

Related definitions from the glossary of financial terms

Accrued interest  •  Bond  •  Coupon  •  Dirty price  •  Discounting  •  Present value  •  Yield to maturity

Related articles

How to Calculate the Price of a Coupon Bond: A Comprehensive Guide   •   Measuring Interest Rate Risk and Credit Risk for Bonds: Exploring Duration, Convexity, and PVBP

Related calculators

Bond price calculator   •   Bond yield calculator   •   Date calculator

Related financial formula

Yield of a coupon bond