Suppose you purchased $300$ shares of the Hon Hai Precision Manufacturing Co $($aka Foxconn, one of the world's largest contract assembler of phones and TVs$)$ six months ago. At the time the shares were trading at $113$ Taiwanese dollars. You sold your shares today for TWD $102$ per share and reconverted your proceeds into dollars at USDTWD $31\mathrm{.}1450,$ earning a return of $5\mathrm{.}2\%.$ To earn this return, what exchange rate did you use when initially buying the krona?

Note: this probably is the most challenging problem of the assignment. To solve, you must work backwards.