An American plane engines manufacturer has exported plane engines to the UK worth five hundred thousand UK pounds $(500,000).$ Because the export was invoiced in UK pounds the American firm was exposed to transaction risk and therefore purchased a put option on the British pounds for premium of $$0\mathrm{.}02$ per pound. The strike price for the transaction was $$1\mathrm{.}30$ per pound. If at the time the US firm exercised its right the pound was selling for $$1\mathrm{.}35,$

$(1)$ Calculate the revenue received by the US firm on the export to UK in US dollars

$($ii$)$ Calculate the revenue and profit received by the financial intermediary which sold the put option to the US exporter