$1.$Suppose that Arthur deposits $$300$ on the $5$th of each month. Interest compounds monthly on the $10$th of each

month, at an APR of $4\%.$ Arthur would like the account balance to reach $$20,000$ on January $15$th $2026.$

Determine how much money Arthur should initially deposit so that he achieves his goal. Round your answer to

two decimal places. $2.$Suppose that Arthur$$s initial deposit is $$2000.$ He makes regular deposits on $5$th of each month. Interest compounds

on the $1$st and $20$th of each month, at an APR of $10\%.$ arthur would like the account balance to reach $$20,000$ on

January $15$th $2026.$

Determine how much money Arthur should deposit regularly so that he achieves his goal. Round your answer

to two decimal places.