Currency Forward Rate Calculator (Interest Parity, PPP & Cross Rates)

This page computes three different things that get confused with one another constantly.

The forward rate comes from covered interest rate parity. It is set entirely by the interest rate differential between the two currencies, enforced by arbitrage, and it is a real price available in the market. It embeds no view whatsoever about where the currency is going.

The PPP forecast comes from relative inflation. It is a long-run theory about where spot might drift, it holds poorly over anything under a decade, and it is not tradeable.

The cross rate simply derives a third pair from two quotes against a common currency.

The most consequential misunderstanding in FX is treating the forward as a prediction. A currency at a forward premium is not expected to appreciate; it is a currency whose interest rate is lower.

Covered interest rate parity:

If this did not hold, you could borrow in one currency, convert, deposit in the other and lock in the forward for a risk-free profit. Arbitrage closes the gap, which is why the forward is a price rather than an opinion.

Purchasing power parity:

Structurally similar, but driven by inflation rather than interest rates, and carrying no arbitrage enforcement at all.

Cross rate, from two quotes against a common currency:

EUR/USD 1.0800, USD 4%, EUR 2%, one year:

• Forward: 1.0800 × (1.04 ÷ 1.02) = 1.1012
• Forward points: 212 pips
• The euro trades at a forward premium, because it is the lower-yielding currency
• Annualised move: 1.96%, which is almost exactly the 2 point rate differential -- as it must be

Reversing the differential (USD 2%, EUR 4%): the forward becomes 1.0592, a discount. Nothing about the currencies changed; only which one pays more.

A five-year tenor: the differential compounds to 1.1901, over 1,100 pips from spot.

PPP with 6% quote-currency inflation: the forecast moves to 1.1224, well away from the forward. The two answers diverge because they are answering different questions.

Cross rate: with GBP/USD at 1.2800, EUR/GBP = 1.0800 ÷ 1.2800 = 0.8438.

• Bid-offer spreads. Real forwards are quoted two-way, and the tradeable rate differs from this mid.
• Credit and counterparty terms, including collateral, which move real forward pricing away from textbook parity.
• Cross-currency basis. Since 2008 covered interest parity has persistently failed by measurable amounts in several pairs, particularly at longer tenors. This calculates textbook parity, not the observed basis.
• Day count and settlement conventions. Real forwards use specific day counts and value dates rather than clean year fractions.
• Capital controls and non-deliverable forwards in restricted currencies.
• Which rate is genuinely risk-free. Reference rates differ by currency and tenor, and the choice moves the answer.
• Whether PPP holds at all. Empirically it has very little predictive power over horizons under five to ten years.
• Central bank intervention and regime shifts.

• Reading the forward as a forecast. It is not. A forward premium reflects a lower interest rate, not an expectation of appreciation. Systematically betting against forwards is the carry trade, and its long history of profits followed by sharp losses is precisely because forwards are not predictions.
• Mixing up base and quote. In EUR/USD the base is the euro and the quote is the dollar. Swapping the two interest rates inverts the premium, as the second scenario shows.
• Using PPP for short horizons. It has almost no explanatory power under five years. It is a long-run anchor, not a trading signal.
• Ignoring the cross-currency basis. Textbook parity has not held exactly since 2008, and the deviation is large enough to matter at longer tenors.
• Comparing a forward with an unhedged forecast. The forward is contractual; a forecast is not. They are not alternatives to be picked between on which number you prefer.
• Applying a cross rate across inconsistent quote conventions. Both legs must be quoted against the same currency in the same direction.

• Covered interest rate parity and relative purchasing power parity are standard international finance relationships with no jurisdictional content.
• The persistent post-2008 deviation from covered interest parity, known as the cross-currency basis, is documented in central bank and BIS research and is noted here rather than modelled.