Formula for Calculating the Price of a Coupon Bond formula
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 calculators
Bond price calculator • Bond yield calculator • Date calculator