Interest Rate Parity Calculator

Understanding Interest Rate Parity (IRP) and Forward Exchange Rates

Interest Rate Parity (IRP) is a foundational economic theory in international finance that governs the relationship between spot exchange rates, forward exchange rates, and nominal interest rates across two national currencies. Under ideal market conditions without capital controls or default risk, the interest rate differential between two countries must equal the percentage difference between the forward exchange rate and the spot exchange rate. All calculations occur locally in your web browser with zero server latency and complete privacy.

When interest rate parity holds, an investor cannot achieve riskless excess returns simply by borrowing funds in a low-interest-rate currency and investing them in a higher-interest-rate currency once currency hedging is applied. If you need to price institutional forward delivery dates with customized day-count conventions and full settlement schedules, check our currency forward calculator. To determine synthetic exchange rates between currency pairs that lack direct market liquidity, utilize our cross exchange rate calculator. Furthermore, to measure historical or expected percentage currency moves over time, visit our currency appreciation depreciation calculator.

Covered vs. Uncovered Interest Rate Parity

Economists and foreign exchange traders differentiate between two distinct variations of interest rate parity: covered parity (CIRP) and uncovered parity (UIP).

Covered Interest Rate Parity (CIRP)

Covered Interest Rate Parity involves using a legally binding forward contract to completely eliminate foreign exchange risk. In covered parity, an investor simultaneously converts spot currency and enters into a forward contract to sell the foreign proceeds at a locked-in exchange rate on the maturity date. Because currency risk is hedged, CIRP is maintained through no-arbitrage conditions enforced by institutional treasuries and proprietary trading desks.

Uncovered Interest Rate Parity (UIP)

Uncovered Interest Rate Parity assumes that investors do not hedge foreign exchange risk with a forward contract. Instead, UIP states that the expected future spot exchange rate equals the theoretical forward rate. According to UIP, currencies with higher interest rates are expected to depreciate against lower-yielding currencies by an amount equal to the interest rate spread. In practice, UIP frequently fails over short and medium horizons due to currency risk premiums, giving rise to popular carry trade strategies where investors profit by holding high-yielding currencies unhedged. To analyze real versus nominal interest rates adjusted for inflation expectations, explore our Fisher effect calculator.

Interest rate parity mathematical formulas

In standard money market conventions (such as interbank deposits up to one year), interest rate parity is calculated using simple annualized interest over the tenor fraction:

In this equation:

• F: Theoretical forward exchange rate (expressed as quote or domestic currency units per one base or foreign currency unit).
• S: Prevailing spot exchange rate.
• i_d: Nominal annualized interest rate in the domestic (quote) currency market, expressed as a decimal.
• i_f: Nominal annualized interest rate in the foreign (base) currency market, expressed as a decimal.
• t: Time to contract maturity in years, typically calculated as $\text{Months} / 12$ or $\text{Days} / 360$ (money market day-count basis).

Continuous compounding variation

In quantitative finance and derivatives pricing (such as the Garman-Kohlhagen currency options model), interest rates are assumed to compound continuously:

Annualized forward premium or discount

The forward premium or discount reflects the percentage difference between the forward rate and spot rate, annualized over the investment period:

If $F > S$, the foreign currency trades at a forward premium (and the domestic currency trades at a forward discount). If $F < S$, the foreign currency trades at a forward discount. The currency with the higher interest rate always trades at a forward discount relative to the lower-interest currency to prevent persistent riskless arbitrage.

Covered interest arbitrage mechanics

When actual quoted market forward rates ($F_{\text{actual}}$) diverge from the theoretical equilibrium rate ($F$), arbitrageurs can lock in guaranteed risk-free profits through covered interest arbitrage (CIA):

• Forward Overvalued ($F_{\text{actual}} > F$): The market forward price of the foreign currency is too expensive. The arbitrageur borrows domestic currency, converts to foreign currency at spot, invests in foreign deposits, and locks in a forward sale at the elevated actual forward rate. Forward proceeds exceed domestic debt repayment, creating riskless profit.
• Forward Undervalued ($F_{\text{actual}} < F$): The market forward price of the foreign currency is too cheap. The arbitrageur borrows foreign currency, converts to domestic at spot, invests in domestic deposits, and buys foreign currency forward at the discounted rate to cover the loan repayment. Excess domestic capital remains as risk-free profit.

Published worked example

Consider an institutional foreign exchange scenario published in corporate finance reference material:

• Spot exchange rate (S): 1.1000 USD per EUR
• Domestic interest rate (USD, $i_d$): 5.00% per annum
• Foreign interest rate (EUR, $i_f$): 3.00% per annum
• Contract tenor: 12 months ($t = 1.0$ year)
• Notional investment amount: $100,000 USD

We calculate the theoretical forward rate using standard simple interest:

The forward points equal $1.1214 - 1.1000 = +0.0214$ (+214 pips). The annualized forward premium on the euro is:

Now assume an actual dealer quotes the forward rate at 1.1500 USD per EUR (an overvalued forward rate). An arbitrageur executes the following steps:

1. Borrows $100,000 USD at 5.00% for 1 year. Total debt owed at maturity equals $105,000 USD.
2. Converts $100,000 USD at spot 1.1000, receiving 90,909.09 EUR.
3. Invests 90,909.09 EUR in European money markets at 3.00%. In 1 year, proceeds grow to 93,636.36 EUR.
4. Sells 93,636.36 EUR forward at the market quote of 1.1500 USD per EUR, locking in proceeds of $107,681.82 USD.
5. Repays the domestic loan of $105,000 USD, leaving a guaranteed riskless net profit of $2,681.82 USD (+2.68% net yield).

Frequently asked questions