Use technology to apply the future value $($FV$)$ function and to answer the following questions.

a$.$ What is the balance in an account after $23$ years with monthly deposits of $$225$ and an APR of $4\%?$

b$.$ If you double the APR in part $($a$),$ is the balance double, more than double, or less than double the balance in part $($a$)?$

c$.$ If you double the number of years in part $($a$),$ is the balance double, more than double, or less than double the balance in part $($a$)?$

a$.$ The balance in the account after $23$ years is $

$($Round to the nearest cent as needed.$)$