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Advanced Financial Management · Interest Rate Risk Management

Forward Rate Agreements (FRA) for CA Final AFM

Updated 5 October 2026 · Fact-checked

A Forward Rate Agreement is an OTC contract that fixes an interest rate for a future period on a notional amount. No principal changes hands. On the settlement date, one party pays the other the discounted difference between the market rate and the agreed rate. Solve it by finding the rate gap, the period, and discounting at the market rate.

Understand Forward Rate Agreements (FRA)

An FRA lets you lock today the interest rate for a loan or deposit that starts in the future. You and a bank agree on a rate, a notional amount and a future period. The loan or deposit itself is never made. Only the interest difference is settled in cash.

The notation m x n (say "m by n") gives the timing in months. In a 3x6 FRA, the contract period starts 3 months from today and ends 6 months from today. So it fixes the rate for a 3-month period that begins 3 months from now. The gap n − m is the contract period. The FRA is settled at the start of that period, that is, at month m.

The buyer of an FRA protects against a rise in rates. The buyer is a borrower hedging future borrowing. If the market rate (the reference rate, such as MIBOR) on the settlement date is above the agreed rate, the seller pays the buyer. If it is below, the buyer pays the seller. The seller of an FRA is typically a lender or depositor who fears a fall in rates.

Interest on the contract period would normally be paid at its end. But the FRA settles at its start. So the difference is discounted back using the market rate. This is the step students forget most often.

An FRA is a customised over-the-counter contract. It has counterparty risk, and the amount, dates and rate can be tailored. Interest rate futures are standardised, exchange-traded and margined. Your net cost after the hedge equals the agreed FRA rate, whichever way the market moves, ignoring basis differences and the bank's spread.

Key rules to remember

Meaning of m x n
FRA starts after m months and ends after n months; contract period = (n − m) months
3x6 means a 3-month rate starting 3 months from now. 6x12 means a 6-month rate starting 6 months from now.
FRA settlement amount
Settlement = [(R_m − R_f) × Notional × (D ÷ 360 or 12-month fraction)] ÷ [1 + R_m × (D ÷ 360 or 12-month fraction)]
R_m = market (reference) rate on settlement date; R_f = FRA rate; use the same time fraction in both numerator and denominator. Use the day count given in the question (360 or 365).
Who pays whom
If R_m > R_f, seller pays buyer. If R_m < R_f, buyer pays seller.
Buyer gains when rates rise; seller gains when rates fall.
Effective result of hedge
Net borrowing cost = actual interest at R_m − FRA receipt (or + FRA payment) = interest at R_f
Compare on the same date. If the FRA is discounted, the receipt can be invested or used to reduce the borrowing at the start.

How to solve Forward Rate Agreements (FRA) questions

Use this order for any FRA question, whether it asks for the settlement, the hedge result or the better choice between FRA and no hedge.

  1. 1Decode the notation. For m x n, note the start (m months) and the contract period (n − m months). Convert to a year fraction.
  2. 2Identify the position. A borrower fearing a rise buys the FRA. A lender or depositor fearing a fall sells it.
  3. 3Note the FRA rate (R_f) and the market rate on the settlement date (R_m). If the question gives several scenarios, handle each separately.
  4. 4Compute the undiscounted interest difference: (R_m − R_f) × notional × time fraction.
  5. 5Discount it by dividing by 1 + R_m × time fraction. This gives the settlement at the start of the period.
  6. 6Decide the direction of payment. R_m above R_f means the buyer receives. R_m below R_f means the buyer pays.
  7. 7If asked for the hedge result, add the FRA cash flow to the actual loan cost or deposit income and show that the effective rate equals R_f. State the conclusion in a line.

Quickest way: Rate gap, then discount

When to use it: Use in numerical MCQs and when you only need the settlement amount and its direction.

  1. Write the gap in rate: R_m − R_f, as a decimal.
  2. Multiply by notional and the period fraction. For 3 months use 3/12 or 90/360 as given.
  3. Divide by (1 + R_m × same fraction).
  4. Sign tells the direction: positive means buyer receives.
  5. Check: the discounted figure must be a little smaller than the undiscounted one.

Common mistakes in Forward Rate Agreements (FRA)

  • Using the full 6 months for a 3x6 FRA.

    Students read 3x6 as a six-month contract.

    Fix: The contract period is n − m = 3 months. The FRA starts at month 3 and ends at month 6.

  • Forgetting to discount the settlement.

    The undiscounted difference looks like the final answer.

    Fix: Settlement is made at the start of the period, so divide by 1 + R_m × fraction. Always include this step unless the question says otherwise.

  • Discounting at the FRA rate instead of the market rate.

    Both rates are in the question and students pick the first.

    Fix: Discount at the market (reference) rate prevailing on the settlement date.

  • Reversing the direction of payment.

    Confusing buyer and seller roles.

    Fix: Buyer is protected against a rise. If the market rate exceeds the FRA rate, the buyer receives. Check with the hedge logic.

  • Mixing time fractions, such as 3/12 in the numerator and 90/360 in the denominator.

    Different data in different lines of the question.

    Fix: Pick one convention given in the question and use it in both places.

  • Treating the notional amount as being paid or lent.

    Confusing an FRA with a loan.

    Fix: Notional is only a base for the interest calculation. No principal moves under the FRA.

Worked examples

Example 1

A company expects to borrow ₹10,00,00,000 for 3 months starting 3 months from now. It buys a 3x6 FRA at 8% p.a. On the settlement date the reference rate is 9% p.a. Calculate the settlement amount and state who pays. Assume a 3/12 year fraction.

Show the solution
  1. Contract period = 6 − 3 = 3 months, so fraction = 3/12 = 0.25.
  2. Rate gap = 9% − 8% = 1% = 0.01.
  3. Undiscounted difference = 0.01 × ₹10,00,00,000 × 0.25 = ₹2,50,000.
  4. Discount factor = 1 + 0.09 × 0.25 = 1.0225.
  5. Settlement = ₹2,50,000 ÷ 1.0225 = ₹2,44,499 (approx).
  6. Market rate is higher than the FRA rate, so the seller pays the buyer.

Answer: The seller pays the company about ₹2,44,499 at the start of the 3-month period.

Example 2

A firm will deposit ₹5,00,00,000 for 6 months starting 6 months from now. It sells a 6x12 FRA at 7% p.a. On the settlement date the reference rate is 6% p.a. Find the settlement amount and show the effective deposit rate. Use a 6/12 year fraction.

Show the solution
  1. Contract period = 12 − 6 = 6 months, fraction = 0.5.
  2. Rate gap = 7% − 6% = 1%. The market rate is below the FRA rate, so the buyer pays the seller (the firm).
  3. Undiscounted difference = 0.01 × ₹5,00,00,000 × 0.5 = ₹2,50,000.
  4. Discount factor = 1 + 0.06 × 0.5 = 1.03.
  5. Settlement = ₹2,50,000 ÷ 1.03 = ₹2,42,718 (approx), received by the firm.
  6. Check: deposit interest at 6% = ₹5,00,00,000 × 0.06 × 0.5 = ₹15,00,000 at the end. The settlement received at the start, grown at 6% for 6 months, is ₹2,42,718 × 1.03 = ₹2,50,000.
  7. Total = ₹15,00,000 + ₹2,50,000 = ₹17,50,000, which equals interest at 7%: ₹5,00,00,000 × 0.07 × 0.5 = ₹17,50,000.

Answer: The firm receives about ₹2,42,718. Its effective deposit return is 7% p.a., the FRA rate.

Exam tips

  • Write the notation decoding first, for example "3x6: starts in 3 months, period 3 months". It earns method marks and prevents period errors.
  • Show the discounting step clearly. Examiners award a mark for it separately.
  • Use the day count and time fraction given in the question, and keep it the same throughout.
  • In hedge-result questions, finish with a line showing the effective rate equals the FRA rate. Case MCQs often test only the direction of payment, so check buyer versus seller first.
  • For FRA versus futures comparisons, state the points: OTC versus exchange-traded, customised versus standardised, counterparty risk versus margining.

Practice questions from Interest Rate Risk Management

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 an FRA?

It means the FRA period starts 3 months from today and ends 6 months from today. The covered period is therefore 3 months. The agreed rate applies to that 3-month period.

How do I calculate the FRA settlement amount?

Multiply the rate gap (market rate minus FRA rate) by the notional amount and the period fraction. Then divide by 1 plus the market rate times the same fraction. If the market rate is higher, the buyer receives.

What is the difference between an FRA and interest rate futures?

An FRA is an over-the-counter contract tailored to your amount and dates, and it carries counterparty risk. Interest rate futures are standardised, traded on an exchange and marked to market with margins. Both fix a future interest rate.

Who should buy and who should sell an FRA?

A borrower who fears rising rates should buy an FRA. A lender or depositor who fears falling rates should sell one. Each locks in the rate they want.