Yield of a coupon bond formula
Description of the Yield of a coupon bond formula
Formula for the calculation of the yield of a coupon bond. The yield \( i \) will be the figure which solves the below equation. It is obtained by iteration.
Formula
\[ P_{g} - \left( \sum_{n=1}^{N} \frac{cpn_{n}}{(1+i)^{t_{n}}}+ \frac{C_{N}}{(1+i)^{t_{N}}} \right ) = 0 \ \]
Symbols
\(C_{N}\ \)
Principal of the bond
\(cpn_{n}\ \)
Nominal coupon of period n
\(i\ \)
Yield
\(P_{g}\ \)
Dirty price
\(t_{n}\ \)
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
Bond • Clean price • Coupon • Yield