One year ago, the exchange rate between the Canadian dollar (CAD) and the euro (EUR) was 1.40 CAD/EUR.

Over the past year, the CAD has depreciated by 12.5% relative to the EUR (i.e., the value of the CAD against the EUR has changed by -12.5%).

What is the CAD/EUR exchange rate today?

Round your final answer to two decimal places. For example, 1.234 should be entered as 1.23.

Question

One year ago, the exchange rate between the Canadian dollar (CAD) and the euro (EUR) was 1.40 CAD/EUR.

Over the past year, the CAD has depreciated by 12.5% relative to the EUR (i.e., the value of the CAD against the EUR has changed by -12.5%).

What is the CAD/EUR exchange rate today?

Round your final answer to two decimal places. For example, 1.234 should be entered as 1.23.

BlackTom AI · Accepted Answer

Depreciation of 12.5% means one Canadian dollar now buys 12.5% fewer euros; therefore apply the percentage change to the value of CAD measured in EUR, then invert to get CAD per EUR.

1) Relevant concepts
- Exchange rate CAD/EUR = number of Canadian dollars required to buy one euro.
- A depreciation of the CAD by 12.5% “relative to the EUR” means the value of one CAD expressed in euros falls by 12.5% (i.e., the CAD’s euro value is multiplied by 1 − 0.125 = 0.875).
- After adjusting the CAD’s value in euros, invert to return to CAD/EUR.

2) Step-by-step reasoning and calculations
- Start with the initial rate: 1 EUR = 1.40 CAD. So 1 CAD = 1 / 1.40 EUR.
  Compute 1 / 1.40 = 0.7142857142857143 EUR per CAD.
- Apply the 12.5% depreciation to the CAD’s euro value:
  New value of 1 CAD in EUR = 0.7142857142857143 × (1 − 0.125)
                            = 0.7142857142857143 × 0.875
                            = 0.625 EUR per CAD.
- Convert back to CAD per EUR (invert):
  New CAD/EUR = 1 / 0.625 = 1.6 CAD per EUR.

3) Why this is correct
- The problem statement explicitly says “the value of the CAD against the EUR has changed by −12.5%,” which refers to the CAD’s value measured in euros. That percentage reduction must be applied to EUR-per-CAD before inverting to get CAD-per-EUR. This yields 1.60 CAD/EUR.

4) Why a common alternative (1.58) is incorrect
- Multiplying the original CAD/EUR rate directly by 1.125 (1.40 × 1.125 = 1.575 → 1.58) assumes the CAD/EUR quote itself increased by 12.5%. That would be correct only if the quote given (CAD/EUR) were the quantity experiencing the 12.5% change; here the statement specifies the CAD’s value (EUR per CAD) fell by 12.5%, so direct multiplication is the wrong operation.

Conclusion: The CAD/EUR exchange rate today is 1.60, matching the provided answer.

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