Paid Plus Change in IBNR

For the purposes of this thread, IBNR = Incurred But Not Reported = IBNP = Incurred But Not Paid = Whatever you are estimating on top of the claims you know about.



Question: The statement was made to me that paid + change in IBNR = Incurred plus total IBNR. Can anyone explain why this is true?



More detail: Let's say you come up with an IBNR estimate for January.



Let:

A=Total claims paid in January

B=Total Incurred claims in January

C=Total IBNR for January

D=Total IBNR for the prior month of December

So the statement is that:

A+(C-D) = B+C

Which when I look at it like that boils down to:

A-D=B

Does this make sense? Is this true? Is there a good way to explain this to a non-Actuary?

Paid Plus Change in IBNR