During Jack's first year at college, his father had been sending him $$110$ per month for incidental expenses. For the sophomore year, his father decided instead to make a deposit into a savings account on August $1$ and have his son withdraw $$110$ on the first of each month from September $1$ to May $1.$ If the bank pays $3\%$ interest compounded monthly, how much should Jack's father deposit?

Jack's father should deposit $

$($Do not round until the final answer. Then round to the nearest cent as needed.$)$