$1.$ Suppose that Arthur makes no initial deposit. He makes regular deposits of $$1,000$ on the $5$th of each month. Interest compounds on the last day of each month at an APR of $6\%.$ Arthur would like the account balance to eventually reach $$40,000.$ Determine the month and year on which Arthur will achieve his goal. Your answer must be in the form $$Month$,$ Year.$($Bonus point if the correct day is given, and the final answer is presented in the form $$Month$,$ Day, Year.$)2.$Suppose that Arthur$$s initial deposit is $$12000.$ He deposits $$300$ on the $5$th of each month. Interest compounds

annually on the $31$st of December. Arthur would like the account balance to reach $$20,000$ on January $15$th $2026.$

Determine the interest rate required so that Arthur achieves his goal. Round your answer to two decimal places.