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to happen or result as a natural growth, addition, etc.
to be added as a matter of periodic gain or advantage, as interest on money.
Law. to become a present and enforceable right or demand.
Contemporary Examples

The petition has accrued 413 signatures so far, as well as multiple comments of support.
Petition Filed Against John Galliano’s Parsons Class Misty White Sidell April 25, 2013

He goes beyond Haass to focus on the immense profits that accrued to American contractors in Iraq and Afghanistan.
The End of the Illusion: America Finally Learns Its Limits Jacob Heilbrunn April 29, 2013

He takes careful sips while passing down the collective knowledge of his ancestors, accrued over countless generations.
Bye Bye Latté, Hello Guayusa: Why The Amazon Holds the Secret to a Cleaner, Healthier Caffeine Brandon Presser August 28, 2014

The show looked and felt nothing like the one that accrued eight seasons of fans.
‘Community’ Review: ‘Repilot’ Is Both an Epic Failure and a Major Success Kevin Fallon January 2, 2014

You can live here and work here, and retire here and collect the social security benefits you’ve accrued.
Republicans Should Support Guest Worker Programs Megan McArdle January 28, 2013

Historical Examples

I would merely sum up the advantages which I conceive have accrued to us by this march.
Life of Wm. Tecumseh Sherman. W. Fletcher Johnson

Here are children in abundance, and what benefit could have accrued to me from his purchasing Vernon?
Lady Susan Jane Austen

Estimate the benefits that would have accrued to this country in the last 250 years if he had been paid 500 to suppress his epic.
Punch or the London Charivari, Volume 150, May 17 1916 Various

But David counted out his debt to her methodically, with the accrued interest.
IT and Other Stories Gouverneur Morris

None could be issued, used as security for loans, or bought up by the government, at less than par plus the accrued interest.
The War With Mexico, Volume II (of 2) Justin H. Smith

verb (intransitive) -crues, -cruing, -crued
to increase by growth or addition, esp (of capital) to increase by periodic addition of interest
(often foll by to) to fall naturally (to); come into the possession (of); result (for)
(law) (of a right or demand) to become capable of being enforced
v.

mid-15c., from Old French acreue “growth, increase, what has grown,” fem. of acreu, past participle of acreistre (Modern French accroître) “to increase,” from Latin accrescere (see accretion). Related: Accrued; accruing. Apparently a verb from a French noun because there is no English verb to go with it until much later, unless the record is defective.