## What is a 'Forward Rate Agreement (FRA)'

Forward rate agreements (FRA) are an over-the-counter contract between parties that determines the rate of interest, or the currency exchange rate, to be paid or received on an obligation beginning at a future start date. The FRA determines the rates to be used along with the termination date and notional value. FRAs are cash settled with the payment based on the net difference between the interest rate and the reference rate in the contract. The notional amount is not exchanged.

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## Breaking Down the 'Forward Rate Agreement (FRA)'

Forward rate agreements involving  interest rates typically see two parties exchange a fixed interest rate for a variable one. The party paying the fixed rate is referred to as the borrower, while the party receiving the variable rate is referred to as the lender.

As a basic example, assume Company A enters into an FRA with Company B in which Company A will receive a fixed rate of 5% for one year on a principal of \$1 million in one year. In return, Company B will receive the one-year LIBOR rate, determined in three years' time, on the principal amount. The agreement will be settled in cash in a payment made at the beginning of the forward period, discounted by an amount calculated using the contract rate and the contract period.

## Forward Rate Agreement Payment Formula

The formula for the FRA payment takes into account five different variables. They are:

FRA = the FRA rate

R = the reference rate

NP = the notional principal

P = the period, which is the number of days in the contract period

Y = the number of days in the year based on the correct day-count convention for the contract

The FRA payment amount is calculated by multiplying two terms together, the settlement amount and the discount factor:

FRA payment = (((R - FRA) x NP x P) / Y) x (1 / (1 + R x (P / Y)))

Assume the following data:

FRA = 3.5%

R = 4%

NP = \$5 million

P = 181 days

Y = 360 days

The FRA payment is calculated as:

FRA payment = (((4% - 3.5%) x \$5,000,000 x 181) / 360) x (1 / (1 + 4% x (181 / 360))) = \$12,569.44 x 0.980285 = \$12,321.64

If the payment amount is positive, the FRA seller pays this amount to the buyer. Otherwise, the buyer pays the seller. As for the day-count convention, if the contract is in British sterling, 365 days are used. In all other currencies the convention is to use 360 days.

The notional amount of \$5 million is not exchanged. Rather the two company involved in this transaction are using that figure to calculate the interest rate differential.

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