Suppose your MasterCard calculates interest using the average daily balance method, and the monthly interest rate is $2\mathrm{.}4\%.$ The itemized billing for the month of August is shown below.

Detail Date Amount

Unpaid balance August $1635$

Charge August $9470$

Charge August $10860$

Charge August $18275$

Payment received August $25665$

Last day of billing period August $31$

Payment due date September $7$

$($a$)$ Find the average daily balance. $

$($b$)$ Find the interest due for this month. $

$($c$)$ Find the total balance owed on the last day of the billing period. $

$($d$)$ This credit card requires a $$15$ minimum payment or $1/24$ of the amount due, whichever is higher. What is the minimum monthly payment due for this month?