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If the EUR/USD exchangerate fell by -0,96%, how much has the USD/EUR exchange rate increased?

According to the below charts the number would be +0,97% (currently) but I cant figure out how these number are related.

EUR/USD

USD/EUR

Please state a formula to convert the percentage change of USD/EUR to the change of EUR/USD.

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closed as off-topic by chollida, olaker Sep 23 '15 at 0:40

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – chollida, olaker
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Hint: if you discount something's price by 50%, you have to raise the price 100% (of the reduced price) to get it back to the original price. Does that help? $\endgroup$ – barrycarter Sep 21 '15 at 20:56
  • $\begingroup$ @barrycarter As stated in the question, I would like to see the formula as answer. $\endgroup$ – emcor Sep 21 '15 at 21:45
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    $\begingroup$ Hint: -1+1/(1-0.0096) = 0.0097 $\endgroup$ – Alex C Sep 22 '15 at 2:18
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I just checked Google Finance and the EUR/USD = 1.1190.... for arguments sake lets say it goes up by 0.10 to 1.2190 the percentage change = 1.2190/1.1190-1 = +8.94%

in terms of USD/EUR the beginning quote would be 1/1.1190 = 0.8937 but would be 1/1.2190 = 0.8203 after the EUR/USD went up by 0.10. Therefore the change in terms of USD/EUR = 0.8203/0.8937-1 = -8.21%

@AlexC formula explains it best:

1/(1-0.0821)-1= +8.94% or 1/(1+0.0894)-1= -8.21%

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