Answer to Question #1106 in Math for Gary Stafford

Question

(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

Answer 1

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%