I'd appreciate a little more context behind this question because superficially it sounds like you are writing the content behind a phishing email.
Giving you the benefit of the doubt though...
First of all, it's not a paragraph - it's a single sentence that uses "and" too many times.
Breaking it down & rewording it -
The bill of July was issued on August 2nd and the amount of your bill is $113
I would replace with
"Your bill for July was issued on August 2nd for a total amount of $113".
The bill of July implies there is only a single bill issued in July, and if this is some form of telecoms delayed payment charge, there would be a LOT more bills issued.
and you have a grace period till August 23rd so please make sure to pay it before that date to prevent any barring on your line and to keep your line working.
Remove the first and, starting a new sentence. Till is antiquated,albeit legitimate, with "until" usually preferred on formal documentation.
"You have a grace period until August 23rd to settle your account. Failure to do so could result in your line being barred"
The final paragraph is therefore -
Your bill for July was issued on August 2nd for a total amount of $113.
You have a grace period until August 23rd to settle your account. Failure to do so could result in your line being barred.