On October $23,$ the closing exchange rate of British pounds was $$1\mathrm{.}80.$ Calls which would mature the following January with a strike price of $$1\mathrm{.}85$ were traded at $$0\mathrm{.}10.$ If the exchange rate of British pounds rises to $$2\mathrm{.}00$ prior to the January option expiration date, what is the percentage return on investment for an investor who purchased a call on October $23?$

$40\%$

$45\%$

$50\%$

$55\%$

$70\%$