$24\mathrm{.}6$A In the draft accounts for the year ended $31$ October $2019$ of Thomas P$.$ Lee, garage proprietor, the balance at bank according to the cash book was $894\mathrm{.}68$ in hand.

Subsequently the following discoveries were made:

$(1)$ Cheque number $176276$ dated $3$ September $2019$ for $310\mathrm{.}84$ in favour of G$.$ Lowe Limited has been correctly recorded in the bank statement, but included in the cash book payments as $301\mathrm{.}84.$

$(2)$ Bank commission charged of $169\mathrm{.}56$ and bank interest charged of $109\mathrm{.}10$ have been entered in the bank statement on $23$ October $2019,$ but not included in the cash book.

$(3)$ The recently received bank statement shows that a cheque for $29\mathrm{.}31$ received from $T.$ Andrews and credited in the bank statements on $9$ October $2019$ has now been dishonoured and debited in the bank statement on $26$ October $2019.$ The only entry in the cash book for this cheque records its receipt on $8$ October $2019.$

$(4)$ Cheque number $177145$ for $15\mathrm{.}10$ has been recorded twice as a credit in the cash book.

$(5)$ Amounts received in the last few days of October $2019$ totalling $1,895\mathrm{.}60$ and recorded in the cash book have not been included in the bank statements until $2$ November $2019.$

$(6)$ Cheques paid according to the cash book during October $2019$ and totalling $395\mathrm{.}80$ were not presented for payment to the bank until November $2019.$

$(7)$ Traders' credits totalling $210\mathrm{.}10$ have been credited in the bank statement on $26$ October $2019,$ but not yet recorded in the cash book.

$(8)$ A standing order payment of $15\mathrm{.}00$ on $17$ October $2019$ to Countryside Publications has been recorded in the bank statement but is not mentioned in the cash book.

Required:

$($a$)$ Prepare a computation of the balance at bank to be included in Thomas P$.$ Lee's balance sheet as at $31$ October $2019.$

$($b$)$ Prepare a bank reconciliation statement as at $31$ October $2019$ for Thomas P$.$ Lee.

$($c$)$ Briefly explain why it is necessary to prepare bank reconciliation statements at accounting year

ends.