Here is Kala's credit card statement for the month of June.

Date Transaction Transaction

amount

June $1$ Beginning balance $$2900\mathrm{.}06$

June $7$ Payment $$540\mathrm{.}00$

June $19$ Purchase $$35\mathrm{.}45$

June $26$ Payment $$700\mathrm{.}00$

$($a$)$Use the credit card statement to help fill in the table below. Note that there are $30$ days in June. Also, a purchase increases the unpaid balance, and a payment decreases the unpaid balance.

Date Transaction Transaction

amount Unpaid

balance Number of days at that balance

Unpaid balance $\backslash$times Number of days

June $1$ Beginning balance $$2900\mathrm{.}06$ $$2900\mathrm{.}066$ days $($from June $1$ through June $6)$ $$17,400\mathrm{.}36$

June $7$ Payment $$540\mathrm{.}00$ $$2360\mathrm{.}06$ days $($from June $7$ through June $18)$ $

June $19$ Purchase $$35\mathrm{.}45$ $ $7$ days $($from June $19$ through June $25)$ $

June $26$ Payment $$700\mathrm{.}00$ $ $5$ days $($from June $26$ through June $30)$ $

Total: $30$ days Total: $

$($b$)$Find the average daily balance. Write your answer to the nearest cent.

$

$($c$)$Suppose the credit card company charges an interest rate of $1\mathrm{.}6\%$ on the average daily balance for June found in part $($b$).$ How much interest will be charged? Write your answer to the nearest cent.

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$($d$)$What will Kala's beginning balance be for the month of July $($including the interest for June found in part $($c$))$