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Financial Management · Causes of exchange rate differences and interest rate fluctuations

Interest Rate Parity Formula and Forward Rate Calculation for ACCA FM

Updated 11 October 2026 · Fact-checked

Interest rate parity says the forward exchange rate reflects the interest rate difference between two currencies. The currency with the higher interest rate trades at a forward discount. Calculate it as forward = spot × (1 + interest rate of the counter currency) ÷ (1 + interest rate of the base currency).

Understand Interest Rate Parity

Start with a simple idea. If you could borrow in one currency and invest in another, you would pick whichever pays more. But you must convert money back at some point. The forward rate fixes that future conversion rate today.

Interest rate parity (IRP) says the forward rate adjusts so that you gain nothing from this. Investing in a high-interest currency earns more interest, but that currency is expected to be worth less at the forward date. The gain from interest is cancelled by the loss on exchange. This removes risk-free profit (arbitrage).

So the currency with the higher interest rate is at a forward discount. It buys fewer units of the other currency in the forward market than at spot. The currency with the lower interest rate is at a forward premium.

IRP uses nominal interest rates and gives a forward rate. Do not confuse it with purchasing power parity (PPP). PPP uses inflation rates and predicts the future spot rate. IRP uses interest rates and gives the forward rate. The two are linked through the Fisher effect, which ties interest rates to inflation, so the results are often similar.

In the exam, the rates given are usually annual. If the period is less than a year, use only the part of the annual rate that applies, for example 6/12 of it for six months. Always check the quote direction before you start.

Key rules to remember

Interest rate parity (forward rate)
F₀ = S₀ × (1 + iᶜ) ÷ (1 + iᵇ)
S₀ and F₀ are quoted as units of the counter currency (c) per 1 unit of the base currency (b). iᶜ is the interest rate of the counter currency. iᵇ is the interest rate of the base currency. Both rates are for the period to the forward date.
Interest rate for part of a year
Period rate = annual rate × (months ÷ 12)
Time-apportion the annual rate (annual rate × months ÷ 12) unless the question states otherwise.
Direction rule
Higher interest rate currency → forward discount; lower interest rate currency → forward premium
Use this to check your answer. The forward rate must move in the right direction from spot.
Multi-year forward rate
F₀ = S₀ × [(1 + iᶜ) ÷ (1 + iᵇ)]ⁿ
Use it for n years with annual rates, if the question gives the same annual rate each year.

How to solve Interest Rate Parity questions

Use the same routine for any forward rate question based on interest rates. It stops you inverting the formula.

  1. 1Write the spot rate and read the quote. Identify which currency is the base (1 unit) and which is the counter currency (the units you receive).
  2. 2Write the interest rate of each currency. Use the rates for the period only, for example 6/12 of the annual rate for six months.
  3. 3Put the counter currency's rate on top and the base currency's rate on the bottom: (1 + iᶜ) ÷ (1 + iᵇ).
  4. 4Multiply the spot rate by this ratio to get the forward rate.
  5. 5Check direction. If the base currency has the higher interest rate, it is at a forward discount and buys fewer counter units forward than at spot (forward < spot). If the counter currency has the higher interest rate, the forward rate is above spot.
  6. 6If you are asked for a bid or offer rate, use the correct side of the spot quote and keep the same method.
  7. 7Round at the end to the number of decimal places in the question, usually four, and state the answer clearly with units.

Quickest way: Top-over-bottom check

When to use it: Use it for objective test questions where you need the forward rate in about a minute.

  1. Write the spot quote as counter per 1 base, for example $/£ or £/€.
  2. Multiply spot by (1 + counter rate) ÷ (1 + base rate). Scale rates for the period first.
  3. Sense check: the counter currency has the higher rate? Then the forward number is bigger than spot. The base currency has the higher rate? Then it is smaller.
  4. Compare with the options. Eliminate any with the wrong direction before you do the exact sum.

Common mistakes in Interest Rate Parity

  • Putting the interest rates the wrong way round

    Students memorise the formula without linking it to the quote direction.

    Fix: Always put the counter currency's rate on top. Then check the direction rule: the higher interest rate currency is at a forward discount.

  • Using the full annual rate for a period under a year

    Students rush and forget the forward date is, for example, six months away.

    Fix: Multiply each annual rate by months ÷ 12 before using it in the formula.

  • Confusing IRP with PPP

    Both theories use a similar ratio, and both link currencies to rates.

    Fix: IRP uses interest rates to find the forward rate. PPP uses inflation rates to predict the future spot rate. Check which rates the question gives.

  • Inverting the spot quote

    The question gives £ per $ but the answer is wanted as $ per £, or the reverse.

    Fix: Write down what each number means before you calculate. Invert the spot first if you need to, then apply the formula.

  • Saying the forward rate is a forecast of the future spot rate

    Students treat the forward rate as a prediction.

    Fix: The forward rate is the rate you can lock in today, set by interest rates. It need not equal the actual spot rate later.

Worked examples

Example 1

The spot rate is $1.5000 per £1. The annual interest rate is 6% in the UK and 3% in the US. Calculate the one-year forward rate ($ per £) using interest rate parity.

Show the solution
  1. Base currency is £ and counter currency is $. Spot = 1.5000 $/£.
  2. Counter rate (US) = 3%. Base rate (UK) = 6%.
  3. F₀ = 1.5000 × 1.03 ÷ 1.06.
  4. 1.03 ÷ 1.06 = 0.971698.
  5. F₀ = 1.5000 × 0.971698 = 1.457547, which is 1.4575 to four decimal places.
  6. Check: the UK has the higher rate, so £ is at a forward discount. It buys fewer dollars forward (1.4575 is below 1.5000). This is correct.

Answer: The one-year forward rate is about $1.4575 per £1.

Example 2

The spot rate is €1.2000 per £1. The annual interest rate is 4% in the eurozone and 7% in the UK. Calculate the six-month forward rate (€ per £) using interest rate parity.

Show the solution
  1. Base currency is £ and counter currency is €. Spot = 1.2000 €/£.
  2. Six-month rates: eurozone 4% × 6/12 = 2%. UK 7% × 6/12 = 3.5%.
  3. F₀ = 1.2000 × 1.02 ÷ 1.035.
  4. 1.02 ÷ 1.035 = 0.985507.
  5. F₀ = 1.2000 × 0.985507 = 1.18261, which is 1.1826 to four decimal places.
  6. Check: the UK has the higher interest rate, so £ is at a forward discount. 1.1826 is below 1.2000. This is correct.

Answer: The six-month forward rate is about €1.1826 per £1.

Exam tips

  • Write the quote meaning (for example $ per £) beside the spot rate before you start. Most lost marks come from direction errors.
  • Scale rates for the period. A six-month or three-month forward uses 6/12 or 3/12 of the annual rate.
  • In a written part, explain that IRP removes arbitrage and that the higher-interest currency is at a forward discount. Link it to PPP and the Fisher effect for extra marks.
  • In objective tests, use the direction check to remove wrong options quickly, since an incorrect answer scores zero.
  • If the question asks which rates to use, read carefully. Interest rates mean IRP and forward rates. Inflation rates mean PPP and future spot rates.

Practice questions from Causes of exchange rate differences and interest rate fluctuations

Interest Rate Parity in other exams

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

Interest Rate Parity: frequently asked questions

What is the interest rate parity formula in ACCA FM?

The forward rate F₀ = S₀ × (1 + interest rate of the counter currency) ÷ (1 + interest rate of the base currency). The spot rate is quoted as counter units per one unit of base currency. Use rates for the period to the forward date.

What is the difference between purchasing power parity and interest rate parity?

PPP uses inflation rate differences to predict the future spot rate. IRP uses interest rate differences to calculate the forward rate. PPP is a theory of expected movement, while IRP gives a rate you can fix today through a forward contract.

How do I calculate a forward rate from interest rates?

Take the spot rate and multiply it by the counter currency's interest factor divided by the base currency's interest factor. Adjust the annual rates for the period first. Then check that the currency with the higher interest rate is at a forward discount.

Why does the higher interest rate currency trade at a forward discount?

Investors gain extra interest in that currency, so the forward rate must make up for it. If it did not, they could earn risk-free profit. The forward discount cancels the interest gain.