What is the formula for the forward premium?

The annualized forward premium or discount is: FP% = (Forward Rate - Spot Rate) / Spot Rate times (360 / days) times 100. A positive result is a forward premium; a negative result is a forward discount. For example, spot USD/EUR = 1.10, forward (90 days) = 1.12: FP% = (1.12 - 1.10) / 1.10 times (360/90) times 100 = 0.0182 times 4 times 100 = 7.27% per year.

What is the difference between a forward premium and a forward discount?

A forward premium means the forward rate is above the spot rate: the quote currency is expected to appreciate. A forward discount means the forward rate is below the spot rate: the quote currency is expected to depreciate. Per covered interest rate parity, a currency with higher interest rates tends to trade at a forward discount because its higher rates compensate for the expected depreciation.

How does covered interest rate parity relate to the forward premium?

Covered interest rate parity (CIP) states that the forward premium approximately equals the interest rate differential: FP% = (r domestic - r foreign), where rates are annualized. If EUR rates are 5% and USD rates are 2%, EUR should trade at roughly a 3% forward premium against USD. Arbitrageurs enforce CIP by borrowing in the low-rate currency, investing in the high-rate currency, and covering via a forward contract.

How do I compute the forward rate from the forward premium?

Rearrange the formula: F = S times (1 + FP% / 100 times n / 360). If the spot rate is 1.10, the annualized forward premium is 4%, and the contract is 90 days: F = 1.10 times (1 + 0.04 times 90/360) = 1.10 times 1.01 = 1.111. This is the Mode 2 calculation in this calculator.

Why is the convention 360 days and not 365?

The 360-day convention (money market basis) is standard for most major FX pairs, including USD, EUR, JPY, CHF, and CAD. It simplifies calculations by using a 12-month year of exactly 30 days each. Some currency pairs, particularly GBP, AUD, and NZD, use 365-day (actual/365) conventions. Always confirm which day count convention applies to your specific currency pair and counterparty agreement.

What is the difference between a forward contract and a futures contract?

Both lock in an exchange rate for future delivery, but they differ in structure. Forward contracts are over-the-counter (OTC) agreements customised between two parties with any amount and any settlement date. Futures contracts are standardised, exchange-traded, marked to market daily, and require margin. For corporate FX hedging, forward contracts are more common because they can be tailored to the exact amount and date of the underlying transaction.

Can the forward premium predict future spot rates?

The uncovered interest rate parity (UIP) hypothesis says the forward premium should predict the future change in the spot rate: currencies at a forward discount should depreciate. In practice, this prediction is poor over short horizons (the forward premium puzzle). Over long horizons (10+ years), the relationship is stronger. The forward premium is an arbitrage-free price, not a consensus forecast of where the spot rate will go.

How is the forward premium used in corporate treasury?

A company expecting to receive 1 million EUR in 90 days can sell EUR forward today to lock in the exchange rate. If the forward premium is 3%, the forward rate is approximately 3% above spot, which the company locks in regardless of where spot moves. This eliminates currency risk on the transaction. The cost of this hedge is the difference between the forward rate and the eventual spot rate at settlement.

What inputs does this calculator need?

For Mode 1 (compute the premium): enter the current spot rate, the agreed forward rate, and the contract period in days. The calculator outputs the annualized forward premium or discount as a percentage and identifies whether the quote currency is at a premium or discount. For Mode 2 (compute the forward rate): enter the spot rate, the annualized forward premium percentage (negative for a discount), and the number of days.

Forward Premium Calculator

Enter a spot rate, forward rate, and contract period to calculate the annualized forward premium or discount, or work backwards to find the implied forward rate.

💹 What is a Forward Premium?

A forward premium is the percentage by which a currency's forward exchange rate exceeds its current spot rate, expressed on an annualized basis. When the forward rate is higher than the spot rate, the quote currency is said to be at a forward premium. When the forward rate is lower, the currency is at a forward discount. The forward premium is a fundamental concept in foreign exchange markets and plays a central role in currency hedging, arbitrage pricing, and international capital flows.

Forward premiums arise from interest rate differentials between countries. According to covered interest rate parity (CIP), the forward premium on a currency approximately equals the difference between domestic and foreign interest rates. If EUR interest rates are 5% and USD rates are 2%, EUR should trade at roughly a 3% forward premium against USD. This relationship is enforced by arbitrageurs who borrow in the lower-rate currency, invest in the higher-rate currency, and use a forward contract to lock in the exchange rate for repayment, eliminating any riskless profit.

Corporations use forward premiums and discounts every day to price hedging decisions. An exporter expecting to receive foreign currency in 90 days can compare the spot rate with the forward rate. If the forward rate is at a 2% annualized premium, buying the spot and paying a 2% cost (or simply taking delivery in 90 days and receiving 2% more) helps evaluate whether hedging is economical. Importers face the opposite consideration: a forward premium on the foreign currency makes imports more expensive at the forward rate than at spot.

This calculator covers two directions: computing the forward premium from spot and forward rates, and computing the implied forward rate from a known annualized premium. Both are standard operations in treasury, FX structuring, and the chartered financial analyst (CFA) and financial risk manager (FRM) exam curricula.

📐 Formula

FP% = (F − S) ÷ S × (360 ÷ n) × 100

FP% = annualized forward premium (positive) or discount (negative)

F = forward exchange rate (quote currency per base currency)

S = spot exchange rate

n = number of days to forward settlement

Example: S = 1.10, F = 1.12, n = 90 days: FP% = (1.12 - 1.10) / 1.10 times (360 / 90) times 100 = 7.27% annualized premium

F = S × (1 + FP% ÷ 100 × n ÷ 360)

F = implied forward rate

S = current spot rate

FP% = annualized forward premium (use negative value for a discount)

Example: S = 1.10, FP% = 4%, n = 90: F = 1.10 times (1 + 0.04 times 90/360) = 1.10 times 1.01 = 1.111

📖 How to Use This Calculator

Steps

Select mode - Choose Forward Premium to compute the premium from spot and forward rates, or Forward Rate to find the implied forward rate from a known premium.

Enter spot rate - Enter the current spot exchange rate (e.g. 1.10 for USD/EUR). Use the same quotation convention throughout.

Enter forward rate or premium - In Mode 1 enter the agreed forward rate. In Mode 2 enter the annualized premium percentage (negative for a discount).

Set contract period - Enter the number of days from today's spot settlement to the forward settlement date (e.g. 90 for a 3-month forward).

Read results - The output shows the annualized premium or discount %, the period change %, whether the currency is at a premium or discount, and the rate difference F minus S.

💡 Example Calculations

Example 1 — EUR Forward Premium Against USD (90 days)

Spot USD/EUR = 1.10, Forward (90-day) = 1.12

Period change = (F - S) / S = (1.12 - 1.10) / 1.10 = 0.01818 = 1.818%

Annualize: 1.818% times (360 / 90) = 1.818% times 4 = 7.273% per year

Annualized Forward Premium = 7.27% (EUR at a premium to USD)

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Example 2 — JPY Forward Discount Against USD (180 days)

Spot USD/JPY = 130.00, Forward (180-day) = 128.50

Period change = (128.50 - 130.00) / 130.00 = -1.50 / 130.00 = -1.154%

Annualize: -1.154% times (360 / 180) = -1.154% times 2 = -2.308% per year

Annualized Forward Discount = -2.31% (USD at a discount to JPY in this quotation)

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Example 3 — Computing the Forward Rate from a 6% Annual Premium (60 days)

Spot = 0.80, Annualized Premium = 6%, Contract = 60 days

F = S times (1 + FP% / 100 times n / 360)

F = 0.80 times (1 + 0.06 times 60/360) = 0.80 times (1 + 0.01) = 0.80 times 1.01 = 0.808

Implied Forward Rate = 0.8080

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❓ Frequently Asked Questions

What is a forward premium in foreign exchange?+

A forward premium occurs when the forward exchange rate of a currency is higher than the current spot rate, expressed as an annualized percentage. It means the market prices the currency at a higher value for future delivery than for immediate settlement. The forward premium is calculated as (F - S) / S times (360 / n) times 100, where F is the forward rate, S the spot rate, and n the days to maturity. A negative result is a forward discount.

How do I calculate the annualized forward premium?+

Step 1: Compute the period percentage change: (F - S) / S. Step 2: Annualize by multiplying by 360 / n, where n is the contract days. Step 3: Multiply by 100 to express as a percentage. For example, spot = 1.10, forward = 1.12, 90 days: (1.12 - 1.10) / 1.10 = 0.01818 (period change). Annualized: 0.01818 times (360/90) times 100 = 7.27%.

What causes a forward premium or discount?+

Forward premiums and discounts are primarily driven by interest rate differentials between countries. Covered interest rate parity states that the forward premium on currency A relative to currency B approximately equals the domestic interest rate on A minus the foreign interest rate on B. A country with lower interest rates will have its currency at a forward premium; a country with higher rates will have its currency at a forward discount. Arbitrageurs enforce this relationship.

What is covered interest rate parity?+

Covered interest rate parity (CIP) is the no-arbitrage condition that links spot rates, forward rates, and interest rates: (1 + r d) = (1 + r f) times F/S, where r d is the domestic rate, r f the foreign rate, F the forward rate, and S the spot rate. An approximate form is FP% = r d - r f. CIP holds well empirically in normal market conditions because arbitrageurs would otherwise borrow at the lower rate, invest at the higher rate, and hedge via a forward contract to lock in a riskless profit.

How do companies use the forward premium in hedging?+

A company expecting to receive 1 million EUR in 90 days can lock in the forward rate today. If the EUR is at a 7.27% annualized premium (spot 1.10, forward 1.12), the company knows it will receive USD 1.12 per EUR regardless of where spot moves. This eliminates currency risk. The cost of the hedge is the difference between the forward rate received and the eventual spot rate, which could be positive or negative relative to doing nothing.

What is the difference between a forward premium and an outright forward?+

An outright forward is the actual exchange rate quoted for future delivery (the F in the formula). The forward premium or discount is the percentage difference between the outright forward and the current spot rate, expressed on an annualized basis. Banks often quote the forward as a swap point differential (forward rate minus spot rate, in pips) rather than as an absolute rate. The premium/discount percentage is then computed from the swap points.

Does the forward premium predict future spot rates?+

The uncovered interest rate parity hypothesis predicts that currencies at a forward premium should appreciate, and those at a forward discount should depreciate, by approximately the premium/discount amount. Empirically, this prediction is unreliable over short horizons (the forward premium puzzle: high-interest-rate currencies often appreciate rather than depreciate as predicted). Over long horizons the relationship is stronger but still noisy. The forward rate is an arbitrage-free price, not a consensus forecast.

Why use 360 days in the forward premium formula?+

Most major FX markets (USD, EUR, JPY, CHF, CAD) use a 360-day year convention (money market basis), which simplifies interest calculations by treating each month as exactly 30 days. GBP, AUD, and NZD markets typically use 365 days (actual/365 or actual/actual). Always confirm the day count convention with your bank or counterparty. This calculator uses 360 days, which is the most common convention for the USD-based pairs most users work with.

What is the forward premium puzzle?+

The forward premium puzzle is the empirical finding that high-interest-rate currencies tend to appreciate rather than depreciate against low-interest-rate currencies over short horizons, the opposite of what uncovered interest rate parity predicts. This forms the basis of the carry trade: borrow in low-rate currencies, invest in high-rate currencies, and do not hedge. The carry trade earns positive returns on average but is subject to sudden crashes when risk appetite reverses and the high-rate currency depreciates sharply.

How is the forward premium relevant for CFA and FRM exam preparation?+

Forward premium calculations appear in CFA Level 1 and Level 2 (Economics and Fixed Income sections), FRM Part 1 (Quantitative Analysis and Financial Markets), and the Treasury Management and International Finance modules of many MBA programs. The exam typically asks you to compute the annualized forward premium, identify whether a currency is at a premium or discount, apply covered interest rate parity, or compute the implied forward rate from interest rates. This calculator mirrors those exact calculations.

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📌 Quick Tips

💡A positive forward premium means the forward rate is higher than the spot rate. In direct quotation terms (USD per EUR), a EUR forward premium means the market expects EUR to strengthen against USD over the contract period.

💡The annualized forward premium uses a 360-day year by convention in most FX markets. Some markets, particularly for GBP and some Commonwealth currencies, use a 365-day year. Check the convention for your currency pair.

💡Interest rate parity (covered interest rate parity) implies that the forward premium approximately equals the interest rate differential between the two countries: FP% = (r domestic - r foreign) times 100. Arbitrage keeps these aligned.

💡A forward discount (negative FP%) means the forward rate is below the spot rate. This typically implies the quote currency has higher interest rates than the base currency, per covered interest rate parity.

💡Forward contracts are used to lock in an exchange rate for a future transaction, eliminating currency risk. Companies with known future foreign currency receipts or payments use them to hedge.