Consider an Option to Buy £10,000 for €12,500 Calculate the Current €/£ Spot Exchange Rate

Essay

Consider an option to buy £10,000 for €12,500.In the next period,if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent.On the other hand,the euro could depreciate against the pound by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.

$\begin{array}{lll}&spot Rates&Risk-tree Rates\\S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \\S_{0}\left(\$ / £)\right. & \$ 2.00=£ 1.00&i €4.00 \% \\S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%\end{array}$ Calculate the current €/£ spot exchange rate.