$1.$ William purchased a $$110,000270-$day commercial paper on its date of issue, when the yield was $3\mathrm{.}89\%.$ He sold it $178$ days later when yields had increased to $4\mathrm{.}03\%.$ How much money did William earn on his investment? $$

$2.$ A $90-$day Province of Ontario T$-$bill with a $$35,000$ face value matures on December $11,2022.$ Farrah works for Hearthplace Industries and notices that the company temporarily has some extra cash available. If she invests the money on October $28,2022,$ when the yield is $4\mathrm{.}94\%,$ and sells the T$-$bill on November $25,2022,$ when the yield is $4\mathrm{.}83\%,$ calculate how much money Farrah earned and the rate of return she realized.