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color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
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border-radius: 8px;
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box-shadow: 0 4px 6px rgba(0,0,0,0.05);
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function calculateForwardRate() {
var spotRate = parseFloat(document.getElementById('spotRate').value);
var baseRate = parseFloat(document.getElementById('baseRate').value);
var quoteRate = parseFloat(document.getElementById('quoteRate').value);
var days = parseFloat(document.getElementById('days').value);
var basis = parseFloat(document.getElementById('basis').value);
if (isNaN(spotRate) || isNaN(baseRate) || isNaN(quoteRate) || isNaN(days) || isNaN(basis)) {
alert("Please fill in all fields with valid numbers.");
return;
}
// Convert percentages to decimals (e.g., 5% -> 0.05)
var rBase = baseRate / 100;
var rQuote = quoteRate / 100;
// Calculate time factor
var timeFactor = days / basis;
// Calculate the numerator (Quote Currency Interest)
var numerator = 1 + (rQuote * timeFactor);
// Calculate the denominator (Base Currency Interest)
var denominator = 1 + (rBase * timeFactor);
// Calculate Forward Rate using Interest Rate Parity Formula
var forwardRate = spotRate * (numerator / denominator);
// Calculate Forward Points (Difference between Forward and Spot)
// Usually multiplied by 10,000 for standard pairs or 100 for JPY pairs
// Here we just show the raw numerical difference
var difference = forwardRate – spotRate;
// Determine if it is a Premium or Discount
// If Forward > Spot, the Base currency is at a Premium (if quote rate > base rate usually)
// Actually: If Base Rate Forward > Spot -> Premium
var premiumStatus = "";
if (difference > 0) {
premiumStatus = "Premium";
} else if (difference 100) to adjust decimals dynamically
var decimals = 4;
if (spotRate > 50) {
decimals = 2; // For pairs like USD/JPY
}
document.getElementById('forwardRateResult').innerHTML = forwardRate.toFixed(decimals);
// Forward points usually expressed as simple difference, formatted nicely
var pointsDisplay = difference.toFixed(decimals);
if (difference > 0) pointsDisplay = "+" + pointsDisplay;
document.getElementById('forwardPointsResult').innerHTML = pointsDisplay;
document.getElementById('premiumResult').innerHTML = premiumStatus;
document.getElementById('resultSection').style.display = "block";
}
How to Calculate a Forward Exchange Rate
The forward exchange rate is a crucial concept in international finance, allowing businesses and investors to hedge against currency risk or speculate on future currency movements. It represents the exchange rate agreed upon today for a transaction that will occur on a specific future date.
Understanding Interest Rate Parity
The calculation of a forward exchange rate is based on the theory of Covered Interest Rate Parity (CIRP). This economic theory states that the difference between the forward rate and the spot rate is determined by the interest rate differential between the two currencies involved. In an efficient market, there should be no arbitrage opportunities, meaning you cannot make a risk-free profit by borrowing in one currency, converting it, investing in another, and locking in a forward contract.
The Forward Rate Formula
To manually calculate the forward rate, you need the current spot rate, the interest rates of both currencies and the time period. The standard formula used in our calculator is:
F = S × [ (1 + iq × t/B) / (1 + ib × t/B) ]
Where:
- F = Forward Exchange Rate
- S = Current Spot Exchange Rate
- iq = Interest rate of the Quote currency (the second currency in the pair)
- ib = Interest rate of the Base currency (the first currency in the pair)
- t = Number of days until the forward contract matures
- B = Day count basis (typically 360 for most currencies like EUR and USD, but 365 for GBP)
Example Calculation
Let's look at a realistic example of calculating a 3-month (90 days) forward rate for the EUR/USD currency pair.
- Currency Pair: EUR/USD (Base: EUR, Quote: USD)
- Spot Rate (S): 1.1000
- USD Interest Rate (iq): 5.00% (0.05)
- EUR Interest Rate (ib): 3.50% (0.035)
- Time (t): 90 days
- Basis (B): 360
Step 1: Calculate the interest factors for both currencies.
USD Factor: 1 + (0.05 × 90/360) = 1 + 0.0125 = 1.0125
EUR Factor: 1 + (0.035 × 90/360) = 1 + 0.00875 = 1.00875
Step 2: Apply the formula.
F = 1.1000 × (1.0125 / 1.00875)
F = 1.1000 × 1.003717
F ≈ 1.1041
In this example, the forward rate (1.1041) is higher than the spot rate (1.1000). This means the EUR is trading at a forward premium because the interest rate of the quote currency (USD) is higher than the base currency (EUR).
Premium vs. Discount
The relationship between the interest rates determines whether the forward rate trades at a premium or a discount to the spot rate:
- Premium: If the interest rate of the Quote currency is higher than the Base currency, the forward rate will be higher than the spot rate.
- Discount: If the interest rate of the Quote currency is lower than the Base currency, the forward rate will be lower than the spot rate.
Why is this calculation important?
Importers and exporters use forward contracts to lock in costs. For example, if a US company needs to pay 1 million Euros in 90 days, they face the risk that the Euro might become more expensive. By calculating the forward rate and entering a contract, they know exactly how many Dollars they will need to pay, regardless of market volatility.
Frequently Asked Questions
What are Forward Points?
Traders often quote the difference between the spot and forward rate in "points" or "pips" rather than the full rate. In the example above, the difference is 1.1041 – 1.1000 = 0.0041, which equals +41 points.
Which day count basis should I use?
For most major currency pairs (EUR/USD, USD/JPY, USD/CHF), the standard convention is a 360-day year. However, for pairs involving the British Pound (GBP), Australian Dollar (AUD), or Canadian Dollar (CAD), a 365-day basis is typically used.
Does this calculator predict future rates?
No. A forward rate is not a prediction of where the spot rate will be in the future. It is a mathematical derivation based on current interest rate differentials to prevent arbitrage.