The difference between Accrue and Add up

When used as verbs, accrue means to increase, to augment, whereas add up means to take a sum.

Accrue is also noun with the meaning: something that accrues.

check bellow for the other definitions of Accrue and Add up

Accrue as a verb (intransitive):

To increase, to augment; to come to by way of increase; to arise or spring as a growth or result; to be added as increase, profit, or damage, especially as the produce of money lent.
Accrue as a verb (intransitive, accounting):

To be incurred as a result of the passage of time.

Examples:

"The monthly financial statements show all the actual but only some of the accrued expenses."
Accrue as a verb (transitive):

to accumulate

Examples:

"He has accrued nine sick days."
Accrue as a verb (intransitive, legal):

To become an enforceable and permanent right.

Accrue as a noun (obsolete):

Something that accrues; advantage accruing

Add up as a verb (transitive):

To take a sum.

Examples:

"usex Add up the prices and find out how much it will cost."
Add up as a verb (intransitive):

To accumulate; to amount to.

Examples:

"usex If you can save even a couple of dollars per day, it will add up to a lot over a year."
Add up as a verb (idiomatic, intransitive):

To make sense; to be reasonable or consistent.

Examples:

"usex His story just doesn't add up. Why would he have been at the restaurant the day before the event?"