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A *forward rate agreement* (FRA) is a contract where the parties agree that an interest rate (contract rate)

will apply to a certain notional principal during a specified future period of time.

An FRA is generally settled in cash at the beginning of the forward period.

This calculator uses simple interest and 30/360 daycount convention.

The price of an FRA can be derived from an arbitrage condition.

At origination, a FRA is priced at the corresponding implied forward rate from today's yield curve.

For example, a "6 X 12" FRA is priced at today's implied six-month forward, six-month interest rate (_{6}R_{12});

this rate can be calculated using the six-month (_{0}R_{6}) and one-year (_{0}R_{12}) interest rates by solving the following equation.

**(1 + _{0}R_{6} * .5) * (1 + _{6}R_{12} * .5) = (1 + _{0}R_{12} *1)**

The price of FRAs with different maturities can be calculated by setting up similar equations.

For example, the price of a "3 X 6" FRA can be derived if _{0}R_{3} and _{0}R_{6} are known,

a "3 X 12" can be priced if _{0}R_{3} and _{0}R_{12} are know etc.

To value an existing FRA one needs:

- Notional principal
*P* - Contract rate
*C* - Forward period
*t*to_{1}*t*_{2} - Spot or zero coupon interest rates with maturities
*t*and_{1}*t*(denoted_{2}_{0}R_{1}and_{0}R_{2}, respectively).

Pricing Models Page Available is a Swing Java Jar File if you just wish to run the models.