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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

It’s now routine for people to graduate with $200K and even $300K of educational debt, at plus 7% interest, accruing daily.
The Perils of Law School Megan McArdle September 23, 2012

Historical Examples

It is most desirable that these accruing demands should be met without resorting to new loans.
A Compilation of the Messages and Papers of the Presidents, James D. Richardson

In his own pocket he dropped the 85 cents accruing to him by virtue of his chemical knowledge.
The Trimmed Lamp O. Henry

Attempts are constantly made both in the United States and England to take from woman the dower right now accruing to them.
Woman, Church & State Matilda Joslyn Gage

To their thinking, women were occasionally very convenient as being the depositaries of some of the accruing wealth of the world.
Ayala’s Angel Anthony Trollope

Sixty penalties have been reckoned as accruing upon excommunication.
The Mysteries of All Nations James Grant

It does not appear that the accruing interest on this great debt was ever paid out of the revenues of the Empire.
The Turkish Empire, its Growth and Decay Lord Eversley

The only credit I can claim as accruing to me is the glory of commanding troops so valorous.
Famous Firesides of French Canada Mary Wilson Alloway

During the first two or three years the accruing dividends were invested in fruit lands in Jamaica and everything went well.
The History of Cuba, vol. 5 Willis Fletcher Johnson

Money left by deceased prisoners, or accruing from the sale of their effects, will be placed in the Prison Fund.
Martyria Augustus C. Hamlin

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.