# Answer to Question #1106 in Other Math for Gary Stafford

Question #1106

(pound V Euro)& if a currency makes a low at 1.0524 and rises to 1.1926 it has risen 13.33%&

If you invert the currency (Euro V Pound) so 1.0524 low becomes 0.9502 high and 1.1926 becomes a 0.8385 low then its fallen I think 11.764% (trial and error)&

This there an equation which if I know its risen 13.33% one way its a fall of 11.764% the other way?&

Thanks for your helpGary

If you invert the currency (Euro V Pound) so 1.0524 low becomes 0.9502 high and 1.1926 becomes a 0.8385 low then its fallen I think 11.764% (trial and error)&

This there an equation which if I know its risen 13.33% one way its a fall of 11.764% the other way?&

Thanks for your helpGary

Expert's answer

Denote the initial currency course as a, risen as b, the rise as R%, the fall as F%.

Then

((b-a)/a)*100% = R%

& b/a& = R% / 100%& + 1

Invert currency course is 1/a and 1/b, and you have to calculate the following expression:

((1/a - 1/b)/1/a)*100% = F%

or

((b-a)/b)*100% = F%

& (1 - a/b) 100% = F%

(1 - 1/ (R/100 +1))100 = R/ (R + 100) * 100% = F%

Answer:

100% * R/ (R+100) = F%

Then

((b-a)/a)*100% = R%

& b/a& = R% / 100%& + 1

Invert currency course is 1/a and 1/b, and you have to calculate the following expression:

((1/a - 1/b)/1/a)*100% = F%

or

((b-a)/b)*100% = F%

& (1 - a/b) 100% = F%

(1 - 1/ (R/100 +1))100 = R/ (R + 100) * 100% = F%

Answer:

100% * R/ (R+100) = F%

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