This section is from the book "Elementary Banking", by John Franklin Ebersole. Also available from Amazon: Elementary Banking.
A contingent liability is a liability of a secondary nature which becomes actual usually on the occurrence of some act or on the default of another. To illustrate: If a bank rediscounts paper with the Federal Reserve bank, or for that matter with any other bank, which it has carried among its assets, the paper is indorsed by the bank which tenders it for rediscount. In case the payer of the paper defaults, recourse is had to the indorser. In order to show that contingent or conditional liability, when a bank rediscounts paper it usually sets up a liability account called "rediscounts." Contingent assets are of similar character, except, of course, that they are secondary assets which may become actual only on the default of some one or the occurrence of some act. Many banks, when rediscounting, set up contingent assets to offset the contingent liability previously mentioned. The entries with respect to rediscounts will be brought out further under discussion of borrowings from Federal Reserve bank.
 
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