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Interest Rate Parity Formula and Calculator

Calculator No. 01-9391 · Updated · Formula and assumptions shown below

Parity forward rate (domestic per foreign) 1.121359
Forward premium or discount (%)
1.9417 %
Result, rounded to 4 decimal places
Domestic interest rate
5 %
Input
Foreign interest rate
3 %
Input
You enter
Domestic interest rate (%), Foreign interest rate (%), Spot rate (domestic per foreign), Time to maturity (years)
You get
Parity forward rate (domestic per foreign), Forward premium or discount (%) (%)
Rounding
6 dp · 4 dp

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

The interest rate parity formula calculates the forward exchange rate implied by two currencies’ interest rates and their spot exchange rate. Enter the domestic and foreign annual interest rates, the spot rate, and the time to maturity to estimate the parity forward rate and compare it with a quoted forward rate.

Formula

Under covered interest rate parity, the forward exchange rate equals the spot exchange rate multiplied by the domestic interest-growth factor and divided by the foreign interest-growth factor:

F = S × (1 + rd)T ÷ (1 + rf)T

  • F is the parity forward rate, expressed as units of domestic currency per one unit of foreign currency.
  • S is the spot exchange rate, using that same quotation convention.
  • rd is the domestic annual interest rate as a decimal.
  • rf is the foreign annual interest rate as a decimal.
  • T is the time to maturity in years.

The calculator accepts interest rates as percentages, so it divides each by 100 in the formula. Its annual growth-factor form assumes annual compounding. The second output is the forward premium or discount relative to spot: (F ÷ S − 1) × 100. A positive result means the foreign currency’s forward price is above its spot price in this quotation; a negative result means it is below.

Worked Example

Using the defaults—domestic rate 5%, foreign rate 3%, spot rate 1.10 domestic currency per foreign unit, and a one-year maturity:

  1. Convert the rates to decimals: rd = 0.05 and rf = 0.03.
  2. Calculate the domestic factor: (1 + 0.05)1 = 1.05.
  3. Calculate the foreign factor: (1 + 0.03)1 = 1.03.
  4. Calculate the parity forward rate: 1.10 × 1.05 ÷ 1.03 = 1.121359, rounded to six decimal places.
  5. Calculate the forward premium: (1.121359 ÷ 1.10 − 1) × 100 = 1.9418%.

The estimated parity forward rate is 1.121359 domestic currency per foreign unit, and the forward rate is about 1.9418% above spot in this example.

What Interest Rate Parity Means

Interest rate parity (IRP) describes a relationship between exchange rates and interest rates in two currencies. The basic economic idea is that, under the model’s assumptions, an investor should not be able to obtain a risk-free gain simply by switching currencies, investing at one interest rate, and locking in the exchange rate for converting the investment back.

Covered interest rate parity uses a forward contract to lock in that future conversion rate. The formula therefore gives a theoretical forward rate consistent with the spot rate and the two interest rates. It does not forecast where the spot exchange rate will actually be in the future.

How to Use and Read the Calculator

Use a consistent exchange-rate quotation throughout. Here, the spot rate must be domestic currency per one unit of foreign currency. If a quoted rate is in the opposite direction, invert it before entering it: a quote of 0.91 foreign units per domestic unit corresponds to about 1 ÷ 0.91 = 1.0989 domestic units per foreign unit.

  • Enter the interest rates for the currencies named domestic and foreign in your chosen quotation.
  • Enter the spot exchange rate in domestic-per-foreign units.
  • Enter the maturity in years; for example, six months is 0.5 years.
  • Read the first result as a theoretical forward quote in the same units as spot.

“Domestic” and “foreign” are labels tied to the quote, not fixed descriptions of a particular country. If you reverse the currency pair, the roles and quote change. Keep the interest rates matched to the currencies after changing the quote.

Covered and Uncovered Parity

Covered interest rate parity (CIP) is the relationship represented by this calculator: the future exchange rate is covered by a forward contract. In real transactions, the forward quote can also reflect market conditions, transaction costs, credit and funding considerations, collateral arrangements, and other constraints. The calculated rate is a benchmark, not necessarily the price available to a particular participant.

Uncovered interest rate parity is a related theoretical idea that compares interest-rate differences with expected changes in the future spot rate, without using a forward contract to lock in conversion. It involves expectations about future exchange rates and is not calculated by this tool. Confusing the two can lead to the misconception that the IRP formula predicts the future spot price.

Assumptions and Limitations

The calculation uses annual compounding for both interest rates and treats the rates as constant over the chosen period. It assumes the input rates refer to comparable investments and maturities. Actual money-market conventions may use different day-count rules, compounding frequencies, settlement dates, or quoted rate definitions; those details can change a market calculation.

The simple formula also omits bid-ask spreads, transaction charges, taxes, funding differences, and counterparty or collateral effects. A gap between a quoted forward rate and the calculated parity rate is not, by itself, proof of a risk-free opportunity: executable prices and the costs and risks of the complete transactions matter. Enter comparable, appropriately dated rates if using the result as a reference.

Frequently Asked Questions

What is the interest rate parity formula?
For covered parity, F = S × (1 + rd)T ÷ (1 + rf)T, where rates are decimals, T is years, and S and F use the same domestic-per-foreign quote.

Does interest rate parity predict the future exchange rate?
No. It calculates a parity-implied forward exchange rate from current inputs. It does not predict the future spot rate.

Why does the higher-interest-rate currency trade at a forward discount?
In the standard covered-parity relationship, the currency with the higher interest rate tends to have a lower forward value relative to its spot value when the quote is expressed in the specified direction. The exact sign depends on the quotation convention and which currency is designated domestic.

How do I calculate the forward rate for six months?
Enter 0.5 for T when the formula uses years. Ensure the rates and spot quote correspond to the same currencies and period.

What is the difference between covered and uncovered interest rate parity?
Covered parity uses a forward contract to lock in the exchange rate; uncovered parity concerns an expected future spot rate and does not lock it in. This calculator applies the covered-parity formula.

This result is an estimate based on the inputs and assumptions shown, not a financial recommendation.

Related

Formula used
in rd | Domestic interest rate | % | 5 | 0.01 | 100
in rf | Foreign interest rate | % | 3 | 0.01 | 100
in spot | Spot rate (domestic per foreign) | - | 1.1 | 0.000001 | 1000000
in yrs | Time to maturity | years | 1 | 0.00274 | 50
out fwd | Parity forward rate (domestic per foreign) | - | spot * (1 + rd / 100) ^ yrs / (1 + rf / 100) ^ yrs | 6
out prem | Forward premium or discount (%) | % | (fwd / spot - 1) * 100 | 4

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

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