Currency Conversion Math: Exchange Rates and Margins
Currency conversion seems simple until you reconcile a credit card statement. Here is the math behind spreads, fees, and effective rates. Currency conversion seems simple: multiply by the exchange rate. But the first time I traveled abroad and tried to reconcile my credit card statement, the numbers did not match my mental estimates. The difference came from margins, fees, and the spread between buy and sell rates. After years of dealing with multiple currencies, here is the math I use to get accurate conversions. The Basic Conversion The basic conversion is straightforward. To convert from one currency to another, multiply the amount by the exchange rate. The exchange rate is the price of one currency in terms of another. If the rate for euros to dollars is 1.08, then 100 euros equals 108 dollars. Amount in target = Amount in source * Exchange rate 100 EUR * 1.08 = 108 USD reading the rate correctly. A rate quoted as EUR to USD means how many dollars one euro buys. A rate quoted as USD to EUR means how many euros one dollar buys. These are reciprocals. If EUR to USD is 1.08, then USD to EUR is 1 divided by 1.08, or about 0.926. I always check which direction the rate is quoted before calculating, because the reciprocal mistake is the most common one I make.