Forward Rate Calculator (Currency Forward Rate)

Compute theoretical FX forward rates from spot and interest rates, or derive implied domestic/foreign interest rates from spot and forward quotes using covered interest parity.

Quoted as domestic currency per 1 unit of foreign currency (e.g. USD per EUR).

months
%

Annualized simple rate in domestic currency.

%

Annualized simple rate in foreign currency.

Day count basis:
Compounding:

What is a forward rate?

In foreign exchange (FX), a forward rate is the exchange rate agreed today for a currency trade that will settle at a future date (for example in 1 month, 3 months, or 1 year). It is the core price in a forward contract or a Forward Rate Agreement (FRA).

Under the covered interest parity condition, the forward rate is linked to the spot rate and the interest rate differential between the two currencies. If domestic interest rates are higher than foreign rates, the foreign currency typically trades at a forward discount (forward rate lower than spot), and vice versa.

Forward rate formula (FX covered interest parity)

Forward rate from spot and interest rates

Let:

  • S = spot exchange rate (domestic currency per 1 unit of foreign currency)
  • F = forward exchange rate for maturity T
  • rd = domestic interest rate (annualized)
  • rf = foreign interest rate (annualized)
  • T = time to maturity in years

With simple interest:

\( F = S \times \dfrac{1 + r_d \, T}{1 + r_f \, T} \)

With annual compounding

\( F = S \times \dfrac{(1 + r_d)^{T}}{(1 + r_f)^{T}} \)

Implied domestic interest rate from spot and forward

Solve for rd (simple interest)

Starting from \( F = S \dfrac{1 + r_d T}{1 + r_f T} \), rearrange:

\( 1 + r_d T = \dfrac{F}{S} (1 + r_f T) \)

\( r_d = \dfrac{\dfrac{F}{S} (1 + r_f T) - 1}{T} \)

Implied foreign interest rate from spot and forward

Solve for rf (simple interest)

From the same parity condition:

\( 1 + r_f T = \dfrac{1 + r_d T}{F/S} \)

\( r_f = \dfrac{\dfrac{1 + r_d T}{F/S} - 1}{T} \)

Worked example

Suppose you have the following market data for EUR/USD:

  • Spot rate S = 1.1000 USD per EUR
  • Domestic rate (USD) rd = 5% per year
  • Foreign rate (EUR) rf = 3% per year
  • Tenor = 6 months = 0.5 years

Using simple interest and T = 0.5:

\( F = 1.1000 \times \dfrac{1 + 0.05 \times 0.5}{1 + 0.03 \times 0.5} = 1.1000 \times \dfrac{1.025}{1.015} \approx 1.1113 \)

The theoretical 6‑month forward rate is about 1.1113 USD per EUR, which is higher than spot. That means the euro trades at a forward premium versus the dollar for this maturity.

Forward premium / discount

Traders often express the difference between forward and spot as a forward premium (if F > S) or forward discount (if F < S), annualized:

Annualized forward premium (approximate)

\( \text{Premium} \approx \dfrac{F - S}{S} \times \dfrac{1}{T} \)

The calculator automatically indicates whether the foreign currency is at a premium or discount and shows the annualized percentage.

Practical tips and limitations

  • The formulas assume no arbitrage and ignore credit, liquidity, and transaction costs.
  • Real market forward quotes may differ slightly due to bid/ask spreads and funding constraints.
  • For very short tenors (e.g. 1 week) or very long tenors (multi‑year), market conventions may use more precise day counts and compounding.
  • Always check which currency is treated as domestic in your quote to avoid inverting the rate by mistake.

FAQ

Is the forward rate a prediction of the future spot rate?

Not exactly. In theory, under some assumptions the forward rate can be an unbiased estimator of future spot, but in practice it mainly reflects the interest rate differential and risk premia. The actual future spot rate can be very different from today’s forward.

How is a forward rate different from a FRA (Forward Rate Agreement)?

A Forward Rate Agreement is an over‑the‑counter derivative on an interest rate (for example 3‑month LIBOR in 6 months), whereas an FX forward is a contract on an exchange rate. Both use the concept of forward rates, but on different underlying variables.

Which day count and compounding should I choose?

Money‑market FX forwards often use Actual/360 or Actual/365 with simple interest. If you are approximating or doing educational exercises, using T = months / 12 with simple interest is usually sufficient. For precise pricing, follow your market’s standard conventions.