Strategic Financial Management · Interest Rate Derivatives

Forward Rate Agreement (FRA): Pricing and Settlement Amount

Updated 11 October 2026 · Fact-checked

A forward rate agreement (FRA) is an over-the-counter contract that fixes an interest rate today for a future period on a notional amount. No principal moves. On the settlement date, the buyer receives or pays the discounted interest difference between the reference rate and the FRA rate. Find the rate, then the difference, then discount it.

Understand Forward Rate Agreements (FRA)

A forward rate agreement lets you lock today the interest rate for a loan or deposit you will take in the future. It is an over-the-counter contract between two parties, usually a company and a bank. The notional principal is never lent or borrowed. It is only used to compute the money that changes hands.

The buyer of an FRA fixes a borrowing rate. The buyer gains if the market rate rises above the FRA rate. The seller fixes a lending rate and gains if the market rate falls below the FRA rate. So a borrower who fears rising rates buys an FRA. An investor who fears falling rates sells one.

The notation 3x6 (said "three by six") means the contract period starts 3 months from now and ends 6 months from now. The contract period is therefore 6 − 3 = 3 months. The first number is the months until the start (the settlement date). The second is the months until the end. A 6x9 FRA covers months 6 to 9. A 1x4 FRA covers months 1 to 4.

Settlement happens at the start of the contract period, not the end. On that date the reference rate (for example MIBOR in India or LIBOR-type benchmarks in older problems) is observed and compared with the FRA rate. The interest difference would naturally be paid at the end of the period. Because it is paid at the start, it is discounted at the reference rate for the contract period.

The FRA rate is the forward rate implied by today's interest rates for the two maturities. If you can borrow for 6 months and for 9 months at known rates, the 6x9 FRA rate is the rate that makes the two routes cost the same. Banks quote it with a small spread. Exam questions usually give the quote or ask you to derive it using simple interest.

Key rules to remember

Contract period: Contract period = Second number − First number (in months); For a 3x6 FRA, the period is 3 months. Settlement is at month 3.
FRA rate (implied forward rate, simple interest): F = [ (1 + R_L × t_L) ÷ (1 + R_S × t_S) − 1 ] ÷ (t_L − t_S); R_L and R_S are annual rates for the long and short maturities. t_L and t_S are the times in years. Use this when the question asks you to price the FRA from spot rates.
Settlement amount (buyer's view): Settlement = N × (RR − FRA rate) × (d ÷ 360) ÷ [1 + RR × (d ÷ 360)]; N is notional, RR is the reference rate at settlement, d is the days in the contract period. Positive means the seller pays the buyer. Negative means the buyer pays the seller. Use 365 instead of 360 if the question says so.
Undiscounted interest difference: N × (RR − FRA rate) × (d ÷ 360); This is the amount that would be due at the end of the contract period. Discount it only if settlement is at the start.
Effective rate after hedging: Effective rate = Actual borrowing rate − (RR − FRA rate) for a buyer; If the loan is priced at the reference rate, the buyer's effective cost equals the FRA rate.

How to solve Forward Rate Agreements (FRA) questions

Use the same sequence for any FRA question, whether it asks for the rate, the settlement amount or the hedged cost.

1Decode the notation. For an m x n FRA, settlement is at month m and the contract period is n − m months. Convert the period into years or days as the question's day basis requires.
2Decide who is hedging. A borrower afraid of rising rates buys the FRA. A lender or depositor afraid of falling rates sells it.
3If the FRA rate is not given, compute it from the two spot rates using the simple-interest forward rate formula.
4Identify the reference rate (settlement rate) at the settlement date. This is the rate that actually prevails.
5Compute the difference RR − FRA rate. If it is positive, the buyer receives. If it is negative, the buyer pays.
6Multiply by notional and by the period fraction. Then divide by 1 + RR × period fraction to discount to the settlement date.
7State the direction and amount clearly: who pays whom, and how much.
8If the question asks about hedging, compare the net cost or return with and without the FRA, and show the effective rate.

Quickest way: Four-line settlement check

When to use it: Use this when the question gives the FRA rate, reference rate, notional and period, and asks only for the settlement amount in an MCQ or the first line of a written answer.

Write the rate gap in decimals: RR − FRA rate. Note its sign first.
Multiply by the notional and by months ÷ 12 (or days ÷ 360). This is the undiscounted amount.
Divide by 1 + RR × the same period fraction. This is the settlement amount.
Sign check: RR above FRA rate means the buyer receives. RR below means the buyer pays. If your sign disagrees, redo the gap.

Common mistakes in Forward Rate Agreements (FRA)

Treating 3x6 as a 6-month contract, or as a contract that starts at month 6
Students read the second number as the length of the contract.
Fix: The first number is the start and the second is the end. Length = second − first. A 3x6 FRA is a 3-month period starting in 3 months.
Forgetting to discount the settlement amount
The interest difference looks complete after multiplying by notional and time.
Fix: Settlement is paid at the start of the contract period, but interest accrues to its end. Always divide by 1 + RR × period fraction unless the question says settlement is at the end.
Getting the direction of payment wrong
Students memorise a sign instead of the logic.
Fix: The buyer is protected against rising rates. If the reference rate is above the FRA rate, the buyer receives. If it is below, the buyer pays.
Using the FRA rate instead of the reference rate in the denominator
Both rates appear in the formula and are easily swapped.
Fix: Discounting uses the reference rate prevailing at settlement, because that is the market rate on that date.
Using the wrong period in the forward rate formula, such as dividing by t_L instead of t_L − t_S
Students copy the long-period time from the compound factor.
Fix: The forward rate applies only to the gap between the two maturities. Divide by (t_L − t_S) in years.
Ignoring the day-count basis given in the question
Students use 360 by habit.
Fix: Use the basis the question states. If it says 365 days, use d ÷ 365 throughout, including in the discount factor.

Worked examples

Example 1

A company will need to borrow ₹10,00,00,000 for 3 months starting 3 months from now. To hedge, it buys a 3x6 FRA at 7.20% p.a. At settlement, the reference rate is 8.00% p.a. Take 90 days in the period and a 360-day year. (a) Compute the FRA settlement amount. (b) Show the company's effective borrowing rate if it borrows at the reference rate.

Show the solution

Notation: 3x6 means settlement at month 3 and a 3-month contract period (90 days). The company is a borrower, so it is the FRA buyer.
Rate gap: RR − FRA rate = 8.00% − 7.20% = 0.80% = 0.008. It is positive, so the buyer receives.
Undiscounted amount = 10,00,00,000 × 0.008 × 90/360 = 10,00,00,000 × 0.002 = ₹2,00,000.
Discount factor = 1 + 0.08 × 90/360 = 1.02.
Settlement amount = 2,00,000 ÷ 1.02 = ₹1,96,078 (approx.), received by the company at the start of the period.
Hedge check: the company borrows ₹10 crore at 8%. Interest for 3 months = 10,00,00,000 × 0.08 × 0.25 = ₹20,00,000.
The FRA receipt of ₹1,96,078, invested for 3 months at 8%, grows to 1,96,078 × 1.02 = ₹2,00,000 (approx.).
Net interest cost = 20,00,000 − 2,00,000 = ₹18,00,000. Effective rate = 18,00,000 ÷ 10,00,00,000 × 4 = 7.20% p.a.

Answer: The seller pays the company about ₹1,96,078 at the start of the period. The company's effective borrowing cost is 7.20% p.a., equal to the FRA rate.

Example 2

The 6-month spot rate is 6.00% p.a. and the 9-month spot rate is 6.50% p.a. (simple interest). (a) Find the 6x9 FRA rate. (b) A company buys this FRA for a notional ₹5,00,00,000. At settlement, the 3-month reference rate is 6.80% p.a. Compute the settlement amount. Round the FRA rate to 7.28% and use a 3-month period of 0.25 year.

Show the solution

Notation: a 6x9 FRA starts at month 6 and ends at month 9. The period is 3 months = 0.25 year.
Long route factor: 1 + 0.065 × 0.75 = 1.04875.
Short route factor: 1 + 0.06 × 0.5 = 1.03.
Ratio = 1.04875 ÷ 1.03 = 1.018204. Subtract 1 to get 0.018204.
FRA rate = 0.018204 ÷ 0.25 = 0.072816, or about 7.28% p.a.
Settlement: the buyer's rate gap = RR − FRA rate = 6.80% − 7.28% = −0.48% = −0.0048. It is negative, so the buyer pays.
Undiscounted amount = 5,00,00,000 × 0.0048 × 0.25 = ₹60,000.
Discount factor = 1 + 0.068 × 0.25 = 1.017.
Settlement amount = 60,000 ÷ 1.017 = ₹58,997 (approx.), paid by the buyer to the seller.

Answer: The 6x9 FRA rate is about 7.28% p.a. With a reference rate of 6.80%, the buyer pays the seller about ₹58,997 at month 6.

Exam tips

Write the notation decoding as your first line. Examiners award marks for stating the settlement date and the contract period.
State the day-count basis you use (360 or 365) and follow the question if it specifies one. Mention it in one line.
Always end with a sentence saying who pays whom and how much. A correct number with no direction can lose marks.
In hedging questions, show the unhedged cost, the FRA settlement and the net effective rate side by side. Then conclude with a clear recommendation.
In MCQs, check the sign and whether the amount is discounted before looking at the options. Wrong options are often the undiscounted figure or the opposite sign.

Practice questions from Interest Rate Derivatives

Forward Rate Agreements (FRA) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Forward Rate Agreements (FRA): frequently asked questions

What does 3x6 mean in a forward rate agreement?

It means the contract period starts 3 months from today and ends 6 months from today. The period is 3 months long. Settlement takes place at the end of month 3, when the contract period begins.

How do you calculate the FRA settlement amount?

Multiply the notional by the gap between the reference rate and the FRA rate and by the period fraction. Then divide by 1 plus the reference rate times the same fraction. A positive result is received by the buyer, and a negative result is paid by the buyer.

Why is the FRA settlement amount discounted?

The interest difference relates to a period that ends later, but the FRA is settled at the start of that period. Discounting at the reference rate converts the end-of-period amount to its value on the settlement date.

Who should buy and who should sell an FRA?

A borrower who fears rising interest rates should buy an FRA to fix the borrowing rate. A lender or investor who fears falling rates should sell an FRA to fix the lending rate.