When the allowance method of recognizing uncollectible accounts is used, how would the collection of an account previously written off affect accounts receivable and the allowance for uncollectible accounts?

Explanation:

When a company sells on credit the company usually creates an Allowance for uncollectible  debts account which is simply a percentage of  credit sales that the company anticipates they will not be collectable, meaning a company anticipates that a certain percentage of customers  will not be able to settle their debts (Bad debts).

When a customer indeed fails to pay their debt, they must be written off.  The Allowance for uncollectible debts account and account receivables must reduced.

When the Debtor that was written off later pays and settles the debt, we first need to reinstate the debtor in the account receivables and Allowance  for uncollectible debt s thus increasing the Receivables and Provision for uncollectible debts account  because both account receivables and Allowance for uncollectible debts were reduced when the debtor was written off.

The journal entry to reinstate the debtor previously written off before recording income received,  

DR Account Receivables  

CR       provision for uncollectible debts

then we need to record the income received

DR Bank/cash received

CR      Account Receivables

to summaries the process when a debtor previously written off pays, we need to reinstate the debtor by increasing account receivable and allowance for uncollactible debts  account then decrease the Account receivable and increasing bank to recognise cash received from a debtor

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explanation:

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