Currency Conversion: Let the Units Tell You Whether to Multiply or Divide

A rate is a ratio with direction

An exchange rate should be written as units of one currency per unit of another. CFPB's covered remittance-disclosure framework distinguishes exchange rate, fees, and recipient amount, helping keep those dimensions separate. In this example, currency A is USD (the home/sender currency) and currency B is EUR (the foreign/recipient currency). If a quote says EUR per USD, multiply a USD amount by that rate to obtain EUR. The USD units cancel, leaving EUR. If the quote instead says USD per EUR, divide the USD amount by it. This unit-cancellation method is more dependable than remembering a universal rule to multiply. No such universal rule exists without the quote direction. The example uses USD and EUR with invented exchange rates, not current foreign-exchange quotes.

Supporting references: 1. CFPB: Regulation E remittance disclosures

Hold the sender's total outlay constant

A fair cost comparison must specify whether the amount being compared is the converted principal or the total money paid. If the sender has a fixed budget, deduct any fee charged in the sender's currency before converting the remainder. The worked example uses a total budget of USD 1,000. One quotation deducts USD 10 and converts at 0.90 EUR per USD; the other deducts USD 20 and converts at 0.91 EUR per USD. The two rows report EUR received. Comparing the exchange rates alone misses the sender fee. Comparing equal converted principal while ignoring an extra fee would instead allow one quotation to use a larger total budget, which answers a different question.

Keep each deduction in its own currency

A sender-side charge denominated in USD cannot be subtracted directly from a recipient amount denominated in EUR. Convert it consistently or place it before conversion, depending on the actual charging rule. A recipient-side deduction in EUR belongs after conversion. Taxes or third-party charges require the same unit discipline. Write a short chain showing budget, sender deductions, converted amount, and recipient deductions. Every step should preserve a meaningful currency unit. This also makes it easier to identify which part of the difference comes from the rate and which comes from charges. The example omits recipient deductions, but that simplification is explicit so the final number is not mistaken for a guarantee of every recipient's actual credited balance.

Invert a quotation carefully

The inverse of a quote is one divided by its value. A rate of 0.90 EUR per USD corresponds mathematically to its reciprocal in USD per EUR. That reciprocal is not automatically the provider's available reverse-conversion rate, because an actual two-way exchange can use different buy and sell terms. Rounding a reciprocal too early can also create discrepancies. Preserve precision while converting, then round the final currency amount according to the relevant display convention. A worksheet should label the quote direction in every column rather than rely on the order of currency names alone. This makes a mistaken inversion visible before it turns a sensible savings amount into an implausible foreign-currency result.

Compare recipient money and timing together

CFPB's public explainer on sending money abroad highlights costs and the amount received. Those are useful comparison concepts, while the regulation supplies the covered US disclosure context. Neither source makes the invented quotations here available or establishes protections for every currency transaction. A real comparison should also check when funds become usable and whether disclosed amounts depend on estimates or excluded charges. The table isolates a fixed sender budget and two fee-rate combinations; it does not recommend a provider. Its enduring method is to align the spending boundary, write exchange-rate units explicitly, and apply charges in the correct currency. That produces an interpretable result instead of allowing an attractive rate alone to stand in for the whole transfer.

Supporting references: 2. CFPB: Problems sending money to another country?

Limits of this analysis

• Quoted rates and fees are invented and may change before execution.
• Recipient deductions and other taxes are excluded.
• US remittance disclosures apply only within their covered scope.