Advanced Financial Management · The use of financial derivatives to hedge against interest rate risk

Forward Rate Agreements (FRAs) for ACCA AFM

Updated 11 October 2026 · Fact-checked

A forward rate agreement (FRA) is an over-the-counter contract that fixes the interest rate on a future loan or deposit. You compare the agreed FRA rate with the actual market rate at settlement. The bank pays or receives the difference on the notional amount, discounted, so you pay the net fixed rate.

Understand Forward Rate Agreements (FRAs)

A forward rate agreement lets you fix today the interest rate for a future period. It is an agreement with a bank, not a loan. The loan or deposit itself is arranged separately in the market. The FRA only settles the difference in interest.

FRAs are quoted as mXn, for example 3v9. The first number is when the FRA period starts, in months from today. The second number is when it ends. A 3v9 FRA starts in 3 months and ends in 9 months, so it covers a 6-month loan period starting in 3 months. A 1v4 covers 3 months starting in 1 month.

Banks quote two rates, for example 3v9 at 4.80% - 4.50%. The higher rate is the one you pay if you are a borrower buying the FRA. The lower rate is the one you receive if you are a depositor selling the FRA. The bank always takes the less favourable side for you.

At the start of the FRA period, the reference rate (such as a benchmark like SOFR-based term rates or similar) is compared with the FRA rate. If the market rate is above the FRA rate, the bank pays a borrower. If it is below, the borrower pays the bank. The settlement is paid at the start of the period, so it is discounted at the market rate, because interest would normally be paid at the end.

The net effect for a borrower is that the actual loan cost plus or minus the FRA settlement equals the FRA rate. The hedge removes the gain from falling rates as well as the loss from rising rates. FRAs are tailor-made, so they suit exact amounts and dates, but they cannot be traded away easily and have no upside.

Key rules to remember

Settlement amount (paid at start of period): Settlement = N × (Market rate − FRA rate) × (m ÷ 12) ÷ [1 + Market rate × (m ÷ 12)]; N is the notional amount, m is the length of the FRA period in months. Positive means the bank pays a borrower; negative means the borrower pays the bank.
Undiscounted interest difference: N × (Market rate − FRA rate) × (m ÷ 12); This is the amount you would pay at the end of the period. Discount it to get the actual settlement.
Reading mXn: Start = m months from now; End = n months from now; Period = n − m months; 3v9 gives a 6-month period starting in 3 months.
Quote rule: Borrower pays the higher quoted rate; depositor receives the lower quoted rate; Use the rate that is worse for you as the customer.
Effective rate with FRA: Effective cost = Actual interest paid on loan ± FRA settlement (compounded to end of period); If hedged properly it equals the FRA rate, plus any margin over the reference rate on the loan.

How to solve Forward Rate Agreements (FRAs) questions

Use this method for any FRA question, whether it asks for settlement, effective rate or a comparison with other hedges.

1Decide whether you are a borrower or a depositor. A borrower fears rising rates and buys an FRA. A depositor fears falling rates and sells one.
2Decode the FRA code mXn. Work out when the period starts and its length in months (n − m).
3Pick the FRA rate from the quote. Borrower: higher rate. Depositor: lower rate.
4Find the market rate at settlement. Note whether it is the same basis as the FRA rate, and whether the borrower pays a margin on top.
5Calculate the interest difference: N × (market rate − FRA rate) × m/12. Then discount by dividing by 1 + market rate × m/12 if the question says settlement is at the start of the period.
6Decide the direction. Borrower: market above FRA means receipt; market below means payment. Depositor is the reverse.
7Calculate the effective result. Add the loan interest at the market rate and adjust for the settlement, carried forward to the end of the period at the market rate. Show the net rate equals the FRA rate (plus margin).
8Comment briefly: rate locked, no benefit from favourable moves, and credit risk with the bank. Compare with futures, options or swaps if asked.

Quickest way: Rate gap shortcut

When to use it: Use when the question asks only for the settlement or whether you pay or receive, and time is short.

Write the gap: market rate − FRA rate, in percentage points.
Multiply notional × gap × months/12 to get the end-of-period difference.
Divide by 1 + market rate × months/12 to get the amount paid at the start.
Borrower: positive gap means you receive. Depositor: positive gap means you pay.
To check the effective rate, remember that the hedged rate must come back to the FRA rate. If your answer does not, recheck the sign.

Common mistakes in Forward Rate Agreements (FRAs)

Misreading 3v9 as a 9-month period or a 3-month period.
Students take one of the two numbers as the length.
Fix: Period = second number minus first number. 3v9 starts in 3 months and lasts 6 months.
Using the wrong side of the bank quote.
Students pick the better-looking rate.
Fix: A borrower pays the higher rate. A depositor receives the lower rate.
Forgetting to discount the settlement.
Students copy the futures approach or use the simple interest difference.
Fix: FRA settlement is paid at the start of the period. Divide by 1 + market rate × m/12 unless the question says otherwise.
Getting the direction of payment wrong.
Students do not link the sign to the borrower or depositor position.
Fix: Borrower: market above FRA, bank pays. Depositor: market below FRA, bank pays. Check by asking who is better off in the market.
Using the annual rate for the whole period.
Students forget to scale the rate by months/12.
Fix: Always multiply by m/12 for both the interest and the discount factor.
Saying the FRA protects the borrower from all outcomes and gives upside.
Confusing FRAs with options.
Fix: An FRA is binding. It fixes the rate and removes both gains and losses. Only options keep the upside.

Worked examples

Example 1

A company will borrow ₹50,00,00,000 in 3 months for 6 months. It is worried that rates will rise. The bank quotes 3v9 FRA at 5.20% - 4.90%. At settlement the 6-month market rate is 6.00%. Calculate the FRA settlement and show the effective borrowing rate. Assume the company borrows at the market rate with no margin.

Show the solution

The company is a borrower, so it buys the FRA at the higher rate, 5.20%.
The period is 9 − 3 = 6 months, so m/12 = 0.5.
Market rate 6.00% is above FRA rate 5.20%, so the bank pays the company. The gap is 0.80%.
Undiscounted difference = ₹50,00,00,000 × 0.0080 × 0.5 = ₹20,00,000.
Discount factor = 1 + 0.06 × 0.5 = 1.03.
Settlement received at the start = ₹20,00,000 ÷ 1.03 = ₹19,41,748 (rounded).
Loan interest at the end of the period = ₹50,00,00,000 × 0.06 × 0.5 = ₹1,50,00,000.
The settlement received grows to ₹19,41,748 × 1.03 = ₹20,00,000 at the end of the period.
Net interest cost = ₹1,50,00,000 − ₹20,00,000 = ₹1,30,00,000.
Effective rate = ₹1,30,00,000 ÷ ₹50,00,00,000 × 2 = 5.20%.

Answer: The company receives about ₹19,41,748 at the start of the period. The effective borrowing rate is 5.20%, equal to the FRA rate.

Example 2

A treasurer expects to deposit $8,000,000 in 2 months for 4 months. The bank quotes a 2v6 FRA at 3.40% - 3.10%. At settlement the 4-month market rate is 2.50%. Calculate the settlement and state who pays whom.

Show the solution

The company is a depositor, so it sells the FRA at the lower rate, 3.10%.
The period is 6 − 2 = 4 months, so m/12 = 1/3.
Market rate 2.50% is below the FRA rate 3.10%, so the bank pays the depositor. The gap is 0.60%.
Undiscounted difference = $8,000,000 × 0.0060 × 4/12 = $16,000.
Discount factor = 1 + 0.025 × 4/12 = 1.008333.
Settlement = $16,000 ÷ 1.008333 = $15,868 (rounded).
Check the effective rate: deposit interest at market = $8,000,000 × 0.025 × 4/12 = $66,667. Add $16,000 from the FRA at the end of the period = $82,667.
Effective rate = $82,667 ÷ $8,000,000 × 3 = 3.10%.

Answer: The bank pays the company about $15,868 at the start of the period. The effective deposit rate is 3.10%, the FRA rate.

Exam tips

Write the mXn decode first. Examiners often test whether you know the start date and the period length.
Show the borrower or depositor decision and the bank quote you chose. These are easy marks and the scenario usually hints at them.
Prove the hedge by showing the effective rate equals the FRA rate. It earns marks and checks your arithmetic.
In discussion parts, note the FRA is over the counter, cannot be traded away, has counterparty risk and gives no upside. Contrast with options and futures using the company's facts.
State your assumption on discounting and margins if the question is silent, and keep the working in clear steps.

Practice questions from The use of financial derivatives to hedge against 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 3v9 mean in an FRA?

It means the FRA period starts in 3 months and ends in 9 months. The covered period is therefore 6 months. The rate fixed is for borrowing or depositing over that 6-month period.

How do you calculate the FRA settlement amount?

Multiply the notional by the difference between the market rate and the FRA rate, then by the period in years. Divide this by 1 plus the market rate times the period in years, because settlement is paid at the start of the period. The sign shows who pays.

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

An FRA is an over-the-counter contract with a bank, tailored to your amount and dates. A future is a standardised exchange-traded contract with fixed sizes and dates, and it needs margin and may leave basis risk. Futures can be closed out easily, while an FRA usually cannot be traded away.

Does an FRA protect against both rising and falling rates?

Yes, it fixes the rate either way. A borrower is protected if rates rise but cannot gain if rates fall. If you want to keep the benefit of favourable moves, you need an interest rate option.