An exchange rate can deliver 3% less currency than a benchmark while making the same foreign-currency purchase cost 3.09% more. Both percentages can be correct. The difference is what stays fixed and which amount sits beneath the fraction.
This matters when one comparison describes the amount you receive and another describes the amount you pay. Before calling the numbers inconsistent, check the direction of the exchange rate and the denominator.
First fix the direction of the rate
Suppose the benchmark is 100 foreign units for one home unit, and the offered rate is 97 foreign units for one home unit. Neither rate includes a separate fee in this first example. A higher number is better for someone exchanging home currency into foreign currency, because each home unit buys more.
The relative shortfall is (100 − 97) ÷ 100 = 3%. If you exchange 100 home units, the benchmark would give 10,000 foreign units; the offered rate gives 9,700. The shortfall is 300 foreign units, or 3% of the benchmark receive amount.
Now keep the purchase fixed instead. To buy exactly 10,000 foreign units at the offered rate, you need 10,000 ÷ 97 = 103.0927835 home units. At the benchmark, you would need 100. The extra outlay relative to that benchmark cost is 3.0927835 ÷ 100 = 3.0928%, rounded to 3.09%.
| What stays fixed? | At benchmark rate 100 | At offered rate 97 | Comparison |
|---|---|---|---|
| Spend 100 home units | Receive 10,000 foreign units | Receive 9,700 foreign units | Receive 3% less |
| Receive 10,000 foreign units | Pay 100 home units | Pay approximately 103.09 home units | Pay approximately 3.09% more |
The second row uses the unrounded quotient when calculating the percentage. Actual settlement rounding may slightly change a small transaction’s result. Neither row says the provider charges two separate margins: these are two ways to describe the same pair of rates.
Why taking the reciprocal changes the percentage
The benchmark can also be written as 0.01 home units per foreign unit. The offered rate becomes 1 ÷ 97, approximately 0.01030928 home units per foreign unit. In this direction, a lower number is better for the buyer of foreign currency.
Let b be the benchmark and q the offered rate, both measured in foreign units per home unit. Define s as the receive-side shortfall, written as a decimal. For positive rates where q is below b:
Receive-side shortfall: s = 1 − q / b Extra cost relative to benchmark: b / q − 1 Equivalent expression: s / (1 − s)
For a 3% shortfall, enter 0.03, not 3: 0.03 ÷ 0.97 = 0.030927835, or 3.0928%. A 1% shortfall becomes about 1.0101% extra cost; a 10% shortfall becomes about 11.1111%. The gap grows because the denominator shrinks. Adding 3% back to 97 produces 99.91, not 100.
“Percentage of what?” is part of the answer
For the fixed 10,000-foreign-unit purchase, the extra cost is approximately 3.0928 home units. Divide that by the benchmark cost of 100 and you obtain 3.0928%. Divide it by the actual payment of 103.0928 and you obtain 3%.
Our comparison methodology expresses comparison cost as a share of the sender’s total payment. That answers a different question from “how much more than the benchmark did this purchase cost?” The percentage label should name its denominator. It should not quietly switch between them.
A separate fee needs its own place in the calculation
Suppose the same fixed purchase also carries a hypothetical fee of two home units, added to the converted amount. Total payment is now 10,000 ÷ 97 + 2 = 105.0927835 home units. Its benchmark-equivalent value remains 100, so comparison cost is 5.0927835.
That is 5.0928% of the benchmark cost, but about 4.84599% of the actual total paid. Calling both “the percentage cost” without a denominator would hide a meaningful distinction. This is not a general rule for every fee: if a fee is deducted from a budget or charged as a percentage, first reconstruct the actual cash flows. Our fee-added versus fee-deducted examples show that step.
The rate-only reciprocal formula does not automatically include card charges, delivery fees, taxes or a second currency conversion. It also does not determine whether an offer is suitable or whether the provider is reliable.
A reference rate is a benchmark, not a promised transaction
The arithmetic needs a clearly identified reference rate and timestamp. A rate from a different moment can introduce market movement into what looks like a provider-cost comparison. A published reference also need not be available to a retail customer.
For example, the European Central Bank states that its euro reference rates are informational and discourages using them for transactions. We cite that limitation, not an ECB rate: every numerical rate in this article is invented for the example.
Read a comparison in this order
- Units: is the rate foreign currency per home unit, or the reciprocal?
- Fixed amount: are you holding the sender’s budget or the recipient’s amount constant?
- Denominator: is the percentage based on the reference amount or the actual payment?
- Coverage: does the result include separate fees, taxes and any further conversion?
- Timing: are the offer and reference comparable in time and transaction conditions?
A 3% figure and a 3.09% figure are not automatically competing claims. In this example, they describe the same rate difference from opposite sides of the exchange.
Research note · 20 October 2026. Original constructed calculations; no provider quote or live pricing test. Arithmetic checked using unrounded values, with displayed results rounded as indicated. ECB reference-rate guidance reviewed on this date. The illustration is AI-generated editorial artwork, not transaction evidence. Report a correction. Financial education, not personal financial advice.
