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Financial Management · Hedging techniques for interest rate risk

Forward Rate Agreements (FRAs) for ACCA FM

Updated 11 October 2026 · Fact-checked

A forward rate agreement (FRA) is a contract with a bank that fixes the interest rate on a notional loan or deposit for a future period. At settlement, the bank pays or receives the difference between the market rate and the FRA rate, applied to the notional amount for the period. The net effect is a fixed rate.

Understand Forward Rate Agreements (FRAs)

Interest rates can move before you borrow or deposit. A company that will borrow in three months worries that rates will rise. A company that will deposit cash worries that rates will fall. An FRA removes that worry by fixing the rate now.

An FRA is an agreement with a bank about a notional loan. No money is lent. The loan amount is only used to work out a payment. On the settlement date, the actual market rate (often a benchmark such as SOFR or its equivalent) is compared with the FRA rate. The party who is worse off under the market rate is compensated by the other.

Quotes look like 3v6 or 3v9. The first number is when the notional loan starts, in months from today. The second number is when it ends. So 3v9 means the loan starts in 3 months and ends in 9 months, a 6-month loan. The loan length is the second number minus the first, not the second number alone.

You are quoted two rates, for example 4.50% to 4.20%. The bank lends at the higher rate and pays on deposits at the lower rate. So a borrower uses the higher rate, and a depositor uses the lower rate. Check which side you are on before you start.

An FRA is a separate contract from the real loan. You still borrow at the actual market rate. If rates rise, you pay more on the loan but receive an FRA payment that offsets it. If rates fall, you pay less on the loan but pay the bank on the FRA. Either way, the net cost is close to the FRA rate. You cannot gain from favourable moves. An FRA is a binding agreement, not an option.

Key rules to remember

Meaning of the quote
FRA m v n: loan starts in m months and lasts (n − m) months
3v9 is a 6-month loan starting in 3 months. 6v12 is a 6-month loan starting in 6 months.
Settlement amount
Settlement = Notional × (Market rate − FRA rate) × (months ÷ 12)
Use the loan length in months. Ignore the sign for size; the sign tells you who pays.
Who pays (borrower's FRA)
Market rate > FRA rate: bank pays you. Market rate < FRA rate: you pay the bank.
The reverse applies to a depositor's FRA.
Which quote to use
Borrower: higher rate. Depositor: lower rate.
The bank always deals at the rate that is worse for you.
Effective rate with an FRA
Net rate ≈ FRA rate
Real loan cost plus or minus the FRA settlement gives about the FRA rate. Exam answers often ignore the timing of the payment.

How to solve Forward Rate Agreements (FRAs) questions

Use the same method for any FRA question. Write each step down so you pick up method marks even if you slip on the arithmetic.

  1. 1Decide whether the company will borrow or deposit, and whether it fears a rise or a fall in rates.
  2. 2Read the quote. Work out the start date and the loan length from the m v n notation.
  3. 3Pick the FRA rate: the higher quoted rate for a borrower, the lower for a depositor.
  4. 4Note the notional amount and the actual market rate at the settlement date.
  5. 5Calculate the settlement: notional × rate difference × months ÷ 12.
  6. 6Decide who pays. For a borrower, the bank pays if the market rate is above the FRA rate, and the company pays if it is below.
  7. 7Combine the settlement with the real interest cost to show the net result, which should be close to the FRA rate.
  8. 8Comment briefly if asked: the rate is fixed, you lose any gain from favourable moves, and there is no premium.

Quickest way: Rate gap times months over twelve

When to use it: Use this for Section A and OT case questions that ask only for the settlement amount or who pays.

  1. Find the loan length: second number minus first number.
  2. Choose the FRA rate by your position: higher for borrowing, lower for depositing.
  3. Find the rate gap between market and FRA, in percentage points.
  4. Multiply notional × gap × months ÷ 12.
  5. Check the direction: a borrower receives when the market rate is higher. A depositor receives when the market rate is lower.

Common mistakes in Forward Rate Agreements (FRAs)

  • Using the second number of the quote as the loan length, for example treating 3v9 as a 9-month loan.

    Students read 3v9 as '9 months' and forget the first number is the delay.

    Fix: Always subtract. 3v9 is 9 − 3 = 6 months, starting in 3 months.

  • Using the wrong side of the two-way quote.

    Students pick the first rate quoted without checking whether they borrow or deposit.

    Fix: Borrowers take the higher rate. Depositors take the lower rate. Write 'borrow = high' beside the question.

  • Getting the direction of payment wrong.

    Students memorise a rule without thinking about who gains when rates move.

    Fix: Ask who would be hurt by the market move. A borrower is hurt by higher rates, so the bank pays the borrower when the market rate is above the FRA rate.

  • Forgetting to divide by 12, or using the full year of interest.

    Rates are quoted per year, but the FRA covers only part of a year.

    Fix: Multiply by months ÷ 12 every time. A 6-month loan uses 6 ÷ 12 = 0.5.

  • Saying an FRA lets the company benefit if rates move the right way.

    Students confuse FRAs with interest rate options.

    Fix: State that an FRA is binding. It fixes the rate and removes both the downside and the upside. Options keep the upside but cost a premium.

Worked examples

Example 1

Delta plans to borrow ₹10,00,00,000 in 3 months for 6 months. The bank quotes a 3v9 FRA at 5.20% to 4.90%. Delta buys the FRA. At settlement the market rate is 6.40%. Calculate the FRA settlement and Delta's net interest cost for the 6 months.

Show the solution
  1. Delta is a borrower, so it uses the higher rate: 5.20%.
  2. The quote 3v9 means a loan starting in 3 months and lasting 9 − 3 = 6 months.
  3. Rate gap = 6.40% − 5.20% = 1.20%.
  4. Settlement = ₹10,00,00,000 × 1.20% × 6 ÷ 12 = ₹6,00,000.
  5. The market rate is above the FRA rate, so the bank pays Delta ₹6,00,000.
  6. Actual interest on the real loan = ₹10,00,00,000 × 6.40% × 6 ÷ 12 = ₹32,00,000.
  7. Net cost = ₹32,00,000 − ₹6,00,000 = ₹26,00,000.
  8. Check: ₹10,00,00,000 × 5.20% × 6 ÷ 12 = ₹26,00,000, so the net cost matches the FRA rate.

Answer: The bank pays Delta ₹6,00,000. Delta's net interest cost is ₹26,00,000, equal to 5.20% for 6 months.

Example 2

Sigma expects to receive ₹5,00,00,000 in 6 months and will deposit it for 3 months. It buys a 6v9 FRA quoted at 3.80% to 3.50%. At settlement the market deposit rate is 2.70%. Calculate the settlement, state who pays, and find the effective interest earned.

Show the solution
  1. Sigma is a depositor, so it uses the lower rate: 3.50%.
  2. 6v9 means a loan starting in 6 months and lasting 9 − 6 = 3 months.
  3. Rate gap = 3.50% − 2.70% = 0.80%.
  4. Settlement = ₹5,00,00,000 × 0.80% × 3 ÷ 12 = ₹1,00,000.
  5. The market rate is below the FRA rate. A depositor is hurt by falling rates, so the bank pays Sigma ₹1,00,000.
  6. Interest earned on the actual deposit = ₹5,00,00,000 × 2.70% × 3 ÷ 12 = ₹3,37,500.
  7. Total = ₹3,37,500 + ₹1,00,000 = ₹4,37,500.
  8. Check: ₹5,00,00,000 × 3.50% × 3 ÷ 12 = ₹4,37,500.

Answer: The bank pays Sigma ₹1,00,000. Sigma's effective interest is ₹4,37,500, equal to 3.50% for 3 months.

Exam tips

  • Read the quote notation first. Most lost marks come from the wrong loan length.
  • In objective questions, work out who is borrowing or depositing before you pick the rate. Wrong-answer options are often built from the other side of the quote.
  • In Section C, show the settlement, the real interest and the net cost. Then state that the net cost equals the FRA rate.
  • When asked to evaluate FRAs, give points: rate certainty, no premium, no gain from favourable moves, and flexibility limited by being tailored over the counter.
  • Remember objective questions are marked all or nothing, so check the months and the direction before you submit.

Practice questions from Hedging techniques for interest rate risk

Forward Rate Agreements (FRAs) 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 (FRAs): frequently asked questions

What does FRA 3v9 mean?

It is a forward rate agreement on a notional loan that starts in 3 months and ends in 9 months. The loan therefore lasts 6 months. The rate fixed applies to that 6-month period.

How do I calculate the FRA settlement in ACCA FM?

Multiply the notional amount by the difference between the market rate and the FRA rate, then by the loan length in months divided by 12. Then decide who pays. A borrower receives if the market rate is higher than the FRA rate.

Which rate do I use in a two-way FRA quote?

A borrower uses the higher rate and a depositor uses the lower rate. The bank sets its quote so it earns the spread. Check your position before you choose.

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

An FRA is binding, so it fixes the rate and gives up any benefit from favourable moves. An interest rate option gives the right but not the obligation to deal, so you keep the upside, but you pay a premium.