A U$.$S$.-$based insurance company invested $$6,750,000$ in a euro$-$denominated security when the exchange rate was $$\frac{1\mathrm{.}22}{}.$ The exchange rate is now $$\frac{1\mathrm{.}08}{}.$

a$.$ Explain whether the U$.$S$.$ dollar has appreciated or depreciated against the euro. $(4$ points$)$

b$.$ Calculate the return on the investment for the insurance company based only on the change in the exchange rate. $(10$ points$)$