What is a worked example of USD/CAD vs AUD/USD?
A worked example is a fully specified numerical scenario that shows the steps of a calculation from start to finish. For USD/CAD vs AUD/USD, the goal is not to predict outcomes, but to demonstrate how you can convert between currencies using the quote convention of each pair.
USD/CAD is quoted as “how many Canadian dollars (CAD) equal 1 U.S. dollar (USD).” AUD/USD is quoted as “how many U.S. dollars (USD) equal 1 Australian dollar (AUD).” Because USD is the base currency in one pair and the quote currency in the other pair, you must handle directions carefully.
How does a worked example work for USD/CAD vs AUD/USD?
To keep the example independently verifiable, we assume two exchange rates are given by a data source (not by the article):
- Assumption A: USD/CAD = 1.30 (meaning 1 USD = 1.30 CAD)
- Assumption B: AUD/USD = 0.66 (meaning 1 AUD = 0.66 USD)
We also assume a starting amount and a “path” for conversions. Choose a scenario that makes the math explicit:
- Assumption C: Start with 100 USD.
- Assumption D: Convert USD → CAD using USD/CAD.
- Assumption E: For comparison, convert the resulting CAD back to USD using an additional cross-rate step.
Step-by-step arithmetic
- Convert 100 USD to CAD using USD/CAD.
- 100 USD × 1.30 CAD/USD = 130 CAD
- To compare with AUD/USD, we need USD per AUD (from AUD/USD) and then an implied conversion path between CAD and AUD. One way is to create an assumed implied CAD per AUD using the same assumed rates.
From Assumption B (AUD/USD = 0.66):
- 1 AUD = 0.66 USD
- So 1 USD = 1 / 0.66 AUD ≈ 1.5152 AUD
From Assumption A (USD/CAD = 1.30):
- 1 USD = 1.30 CAD
Combine these to get an implied relation:
- 1 USD ≈ 1.30 CAD and ≈ 1.5152 AUD
- Therefore, 1 AUD ≈ (1.30 CAD) / (1.5152) ≈ 0.8571 CAD
So the implied cross-rate is:
- Assumption F (implied): 1 AUD ≈ 0.8571 CAD
- Convert the 130 CAD into AUD using the implied CAD/AUD.
- 130 CAD ÷ 0.8571 CAD/AUD ≈ 151.6667 AUD
- Convert AUD back to USD using AUD/USD.
- 151.6667 AUD × 0.66 USD/AUD ≈ 100.0 USD
Evidence or example conclusions (and what’s actually learned)
In this specific, fully-assumed scenario, converting USD → CAD and then using the implied link between CAD and AUD returns approximately the original 100 USD. That happens because all rates were assumed to be internally consistent.
The learning point is not that “you can trade profitably,” but that the calculation mechanics depend on:
- the direction of the quote (who is base, who is quote), and
- whether your implied cross-rate is consistent with the assumed pair conventions.
Relevant limitations and risks (material failure modes)
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Quote direction errors change outcomes. If you mistakenly treat USD/CAD as “CAD per USD” but invert it, your conversions will be off. Always restate what the quote means before calculating.
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Costs can break “mathematical consistency.” Even if assumed mid-rates are consistent, real-world conversions can include bid/ask spreads, commissions, or other charges. Those mean the round-trip calculation can lose value.
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Market conditions and data refresh. Assumed exchange rates are fixed only for the example. If you use rates from different times or inconsistent sources, the implied cross-rate may not match, and the worked “round trip” will not return the starting amount.
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Execution and liquidity constraints. The realized conversion depends on where and how the conversion is executed. If the available prices differ from the reference rates, results can diverge.
Verification and next question you can ask
To independently verify this type of worked example:
- Confirm the quote convention for each pair (USD/CAD as CAD per 1 USD; AUD/USD as USD per 1 AUD).
- Redo the arithmetic with your own assumed rates and chosen start amount.
- Check consistency by performing a round-trip using only those assumptions.