Basic Exchange Rate Arithmetic Explained with Illustrations

Introduction
Basic exchange rate arithmetic involves converting one currency to another using the exchange rate. The fundamental formula for currency conversion is:

a × b = c
Where:

• a: Amount in the original currency
• b: Exchange rate
• c: Amount after conversion

These transactions occur on the foreign exchange market (Forex market), where foreign currencies and coins are exchanged for the home currency. Exporters and importers needing foreign currency for business must approach banks that handle such transactions via the Forex market.

Basic Foreign Exchange Rate Arithmetic

Cross Rate
A cross rate refers to the exchange rate between two foreign currencies. It also applies when exchanging other currencies against the US dollar outside the United States. For example, a dealer in Mumbai selling or buying Euros against US Dollars uses cross rates.

Example 1:
Given:

• INR/USD = 86.5008
• USD/EUR = 0.97

To find EUR/INR:

1 Euro = 86.5008 / 0.97 = ₹89.1761

Example 2:
A bank purchases an export bill of £100,000. Inter-bank purchase rates:

• USD/INR = 86.5008
• USD/GBP = 0.82

Calculations:

100,000 GBP = 100,000 / 0.82 = USD 121,951.22
121,951.22 × 86.5008 = ₹10,548,878.05

Thus, the bank purchases £100,000 at ₹10,548,878.05 using the cross rate.

Value Date

Definition:
In foreign exchange, the value date is when a trade is settled—the day currencies are exchanged, not when the rate was agreed upon. Typically, the value date is the maturity date of a spot or forward contract.

Value Date Reference Table:

Key Terms:

• Value Today: Same-day settlement (Cash transaction)
• Value Tomorrow (TOM): Settlement the next day
• Spot: Settlement on the second working day after the transaction date

Forward Rate, Premium, and Discount

Forward Rate:
Used when a currency transaction settles after the spot date. It adjusts the spot rate by a premium or discount.

• Premium: The forward rate is higher than the spot rate, indicating the currency is costlier in the forward market.
• Discount: The forward rate is lower than the spot rate, meaning the currency is cheaper in the forward market.

Calculating Premium/Discount:

1. Identify the spot and forward rates.
2. Subtract the spot rate from the forward rate.
3. Divide the difference by the spot rate.
4. Multiply by 100 to convert to a percentage.

Example 1:
Spot rate (USD/JPY) = 156.02
One-year forward rate = 157.60
Forward premium = [(157.60 – 156.02) / 156.02] × 100 = 1.01%

Example 2:
90-day forward rate (JPY/USD) = 157.60
Spot rate = 156.02
Annualized forward premium = [(157.60 – 156.02) / 156.02] × (90 / 360) × 100
= (1.58 / 156.02) × 0.25 × 100 = 0.25%

Usefulness of Forward Premiums and Discounts

Forward premiums and discounts enable investors and businesses to:

• Anticipate currency movements
• Make informed financial decisions
• Manage currency exchange risks effectively

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