# Par yield

Par yield (or par rate) denotes in finance, the coupon rate for which the price of a bond is equal to its nominal value (or par value).[1] It is used in the design of fixed interest securities and in constructing interest rate swaps.

The par yield c for a n-year maturity fixed bond satisfies the following equation[2]

${\displaystyle {\frac {100c}{1+R(0,1)}}+{\frac {100c}{(1+R(0,2))^{2}}}+\cdots +{\frac {100+100c}{(1+R(0,n))^{n}}}=100.}$

This can be more succinctly expressed with the prices of zero coupon bonds:

${\displaystyle c={\frac {1-P_{n}}{\sum _{k=1}^{n}P_{k}}}}$

Here ${\displaystyle R(0,n)}$ denotes the yield (on annual interest rate basis) of an ${\displaystyle n}$-year zero-coupon bond, and ${\displaystyle P_{n}}$ denotes the price of an ${\displaystyle n}$-year ZCB.