Suppose that a bank enters into an FRA that is designed to ensure it will receive a fixed rate of $6\%$ on a principal of $$100$ million for a $6-$month period starting in $2$ years. The FRA is an exchange where SOFR is paid and $6\%$ is received for the $6-$month period. If $6-$month SOFR proves to be $6\mathrm{.}5\%$ for the $6-$month period, how large will the cash flow to the lender be$?$ When is it received?