Interest Rate Parity: Meaning, Formula and Example

Interest rate parity (IRP) is a no-arbitrage relationship linking interest rates, exchange rates, and forward currency prices. This calculator estimates the forward exchange rate implied by two annual interest rates and a spot rate; enter those rates and the spot quote to see the parity rate and its difference from an observed forward rate.

Formula

The calculator uses the covered interest rate parity formula, in annual effective-rate form:

F = S × (1 + i_h)^T / (1 + i_f)^T

• F is the parity forward exchange rate, measured in quote-currency units per one base-currency unit.
• S is the spot exchange rate in the same quote convention.
• i_h is the home-currency annual interest rate, entered as a percentage and converted to a decimal in the calculation.
• i_f is the foreign-currency annual interest rate, also converted to a decimal.
• T is the time to settlement in years.

The output labeled “observed minus parity rate” is the entered forward quote minus the calculated parity rate. A positive result means the entered quote is numerically above the estimate; it is not, by itself, proof of a trade opportunity.

Worked Example

Using the calculator’s defaults: spot rate S = 1.10 quote-currency units per base-currency unit; home rate = 5% a year; foreign rate = 3% a year; T = 1 year; and observed forward rate = 1.12.

1. Convert the percentages to decimals: i_h = 0.05 and i_f = 0.03.
2. Calculate the interest-factor ratio: 1.05 ÷ 1.03 = 1.0194174757.
3. Multiply by the spot rate: F = 1.10 × 1.0194174757 = 1.1213592233.
4. Rounded to six decimal places, the parity forward rate is 1.121359.
5. Compare the observed quote: 1.12 − 1.1213592233 = −0.0013592233, or −0.001359 rounded to six places.

For one base-currency unit, the example’s implied forward price is about 1.121359 units of the quote currency. The observed forward input is slightly lower, but real-world execution costs and market conditions matter before interpreting any gap.

What Interest Rate Parity Means

IRP describes how currency prices adjust across spot and forward markets when investors can borrow or invest in two currencies. In its covered form, an investor can hedge the future exchange rate with a forward contract. In a frictionless market, converting funds, earning interest, and locking in the conversion back should produce the same result as investing directly in the other currency after hedging.

If the two routes offered different certain returns, market participants could potentially borrow in one currency, invest in the other, and use a forward contract to remove exchange-rate uncertainty. Such covered interest arbitrage would put pressure on borrowing rates, deposits, spot quotes, or forward prices until the discrepancy narrowed. The relationship is therefore an equilibrium benchmark, not a promise that every quote matches exactly.

Covered and Uncovered Parity

Covered interest rate parity uses a forward contract to hedge currency risk. Its relationship can be checked against observable spot rates, forward prices, and interest rates, while accounting for practical market constraints.

Uncovered interest rate parity replaces the locked-in forward rate with an expected future spot rate. It says, in simplified terms, that the interest-rate difference is related to the expected currency movement. Because the future spot rate is unknown and expectations can be wrong, uncovered parity is not a guaranteed arbitrage condition. This calculator addresses covered parity only.

How to Read the Quote and Results

Exchange-rate direction is essential. Here, the spot rate is expressed as quote currency per base currency. If the spot rate is 1.10, one unit of the base currency costs 1.10 units of the quote currency. Reversing the quote convention changes the formula’s presentation; do not enter a reciprocal spot quote while keeping the same currency labels.

Under this convention, a higher home interest rate than foreign interest rate makes the parity forward rate numerically higher than the spot rate, all else equal. This is often described as the base currency trading at a forward discount in this quote convention. Terminology can seem reversed when a source defines the exchange rate in the opposite direction, so compare the actual units rather than relying on “premium” or “discount” alone.

Limits, Costs, and Common Misconceptions

The formula uses annual effective compounding, with the rate applied over the entered fraction or number of years. Market quotations may instead use money-market conventions, different day-count fractions, simple interest, or rates matched to specific deposit and borrowing terms. For short maturities, those convention differences can affect comparisons. The displayed estimate is only as meaningful as the alignment of the inputs.

• Use rates for the same maturity and compatible instruments; a policy rate is not automatically the relevant borrowing or deposit rate.
• Keep the quote convention and currencies consistent across the spot and forward inputs.
• Do not treat a small difference as guaranteed profit. Bid–ask spreads, funding costs, collateral requirements, taxes, transaction costs, and counterparty or settlement risks can affect an actual trade.
• The calculation does not model capital controls, market segmentation, credit differences, liquidity constraints, or forward points quoted under a different convention.

A frequent misconception is that IRP predicts where a currency’s spot price will be in the future. Covered parity calculates a forward price consistent with rates and the current spot quote under the stated assumptions; it is not a forecast of the future spot rate.

Frequently Asked Questions

What is the interest rate parity formula?
In annual effective-rate form, covered parity is F = S × (1 + i_h)^T ÷ (1 + i_f)^T, where the rates and exchange rate use consistent currency definitions.

Does interest rate parity mean exchange rates stay constant?
No. It relates spot and forward exchange rates to interest-rate differences. It does not say that the spot rate remains fixed or predict its future value.

What is the difference between covered and uncovered parity?
Covered parity uses a forward contract to lock in the exchange rate. Uncovered parity uses an expected future spot rate, so it involves uncertainty and is not a risk-free arbitrage relationship.

Why might a market forward rate differ from the calculator result?
Inputs may use different rate or day-count conventions, maturities, or quote definitions. Bid–ask spreads, funding and credit conditions, liquidity, and other market frictions can also matter.

Which interest rates should I enter?
Use comparable borrowing or investment rates for the two currencies and the same horizon as the forward contract. The appropriate rates depend on the transaction and market conventions; this calculator does not look them up.

This calculator is an educational estimate, not financial advice; actual market terms and execution costs can change the result.

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in s | Spot rate (quote currency per base currency) | - | 1.10 | 0.000001 | 1000000
in ih | Home interest rate | % | 5 | 0.01 | 100
in if | Foreign interest rate | % | 3 | 0.01 | 100
in t | Time to forward date | years | 1 | 0.0001 | 50
in f | Observed forward rate (optional comparison) | - | 1.12 | 0.000001 | 1000000
out fp | Parity forward rate | - | s * (1 + ih / 100) ^ t / (1 + if / 100) ^ t | 6
out gap | Observed minus parity rate | - | f - fp | 6