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A forward rate agreement (FRA) is an agreement between two parties to enter into a future contract at a predetermined interest rate. It is a derivative contract, which means its valuation is based on the underlying interest rate. The FRA forward rate agreement formula calculates the theoretical forward interest rate that will be used to determine the settlement of the contract.

The FRA forward rate agreement formula is as follows:

FRA forward rate = (spot rate + FRA rate x (FRA days/360)) x (360/days until settlement)

Where:

– Spot rate is the current interest rate for a particular maturity period

– FRA rate is the fixed interest rate agreed upon in the contract

– FRA days is the period between the start date of the agreement and the settlement date

– 360 is the number of days in a year

The FRA forward rate agreement formula is used to calculate the settlement amount of the FRA contract. The settlement amount is the difference between the actual interest rate and the contracted fixed rate multiplied by the notional amount and adjusted for the period of the contract.

For example, let`s say Party A enters into an FRA contract with Party B for a notional amount of $1 million for a three-month period starting six months from now. The FRA rate agreed upon in the contract is 5%. The spot rate for a three-month period is 4.5%. The FRA days are 90 days, and there are 180 days until settlement.

Using the formula, we can calculate the FRA forward rate as follows:

FRA forward rate = (4.5% + 5% x (90/360)) x (360/180)

FRA forward rate = 4.75%

The FRA forward rate is 4.75%. If the actual interest rate for the three-month period at settlement is higher than 4.75%, Party B will pay Party A the difference multiplied by the notional amount, adjusted for the period. If the actual interest rate is lower than 4.75%, Party A will pay Party B the difference multiplied by the notional amount, adjusted for the period.

In conclusion, the FRA forward rate agreement formula is a crucial component for calculating the settlement amount of an FRA contract. It helps the parties involved in the contract to determine the theoretical forward interest rate that will be used to determine the settlement of the contract. The formula is relatively simple to calculate, but it requires an understanding of the spot rate, FRA rate, FRA days, and the number of days until settlement.