Arbitrage and spot exchange rates

Suppose you trade dollars and euros for a bank that has branches in Boston and Frankfurt. You can electronically transfer the funds between the two

branch locations at no cost$,$ and trading commissions are negligible. The current dollar$-$per$-$euro exchange rate in Boston is $E_{\frac{\text{\$}}{E}UR}^{BO}=1\mathrm{.}5939,$ while

in Frankfurt, it is $E_{\frac{\text{\$}}{E}UR}^{FR}=1\mathrm{.}6235.$

You can make a profit for the bank if you buy euros in

and sell them in

Assuming other foreign exchange traders face the same exchange rates you do$,$ they will buy dollars in

and sell them in

$.$ As a result, the dollar$-$per$-$euro exchange rate in Frankfurt $(E_{\frac{\text{\$}}{E}UR}^{FR})$ will

$,$ and the dollar$-$per$-$euro exchange rate in Boston $($

$E_{\frac{\text{\$}}{E}UR}^{BO}{?}^{BO}$ will $,.$