Probability that a credit card expires within a given 12 months

[msmith]

I could really use help on a problem I cannot solve.

My business accepts credit cards for monthly software subscriptions. One of our biggest challenges is billing failures due to expired credit cards. It "seems" like we have an abnormally high number, but "seems" is meaningless when there is certainly math to help me "know."

So, let's assume:

- Every credit card, when issued, has 36 months before expiration
- We sell a 12-month agreement, and our customers pay by credit card

My question is this: If I sell 100 contracts in January, and January is guaranteed paid (as we know if it went through), what is the probability in each of the following 11 months (February through December) that the credit cards used to sign up in January fail due to expiration?

I hope this is a clear question. And I sincerely appreciate your help.

 

[sinx]

I could really use help on a problem I cannot solve.

My business accepts credit cards for monthly software subscriptions. One of our biggest challenges is billing failures due to expired credit cards. It "seems" like we have an abnormally high number, but "seems" is meaningless when there is certainly math to help me "know."

So, let's assume:

- Every credit card, when issued, has 36 months before expiration
- We sell a 12-month agreement, and our customers pay by credit card

My question is this: If I sell 100 contracts in January, and January is guaranteed paid (as we know if it went through), what is the probability in each of the following 11 months (February through December) that the credit cards used to sign up in January fail due to expiration?

I hope this is a clear question. And I sincerely appreciate your help.

since you submitted this in calculus;
I assume you are looking for a more than simple arithmetic answer,
but does this help?

if you assume that cards expire evenly over 36 months, then 1/3 of them will expire in 12, =33%.
or 11/35 in 11 months (=31%), i.e. the longest one could last would be those bought in january, the shortest those bought 35 months previous.
expiration over each month should also be evenly distributed. i.e. 31%/11=2.82% per month.

 

[JeffM]

I could really use help on a problem I cannot solve.

My business accepts credit cards for monthly software subscriptions. One of our biggest challenges is billing failures due to expired credit cards. It "seems" like we have an abnormally high number, but "seems" is meaningless when there is certainly math to help me "know."

So, let's assume:

- Every credit card, when issued, has 36 months before expiration
- We sell a 12-month agreement, and our customers pay by credit card

My question is this: If I sell 100 contracts in January, and January is guaranteed paid (as we know if it went through), what is the probability in each of the following 11 months (February through December) that the credit cards used to sign up in January fail due to expiration?

I hope this is a clear question. And I sincerely appreciate your help.

I have nothing to say about the math behind sinx's response. But I would be greatly surprised if your figures are not higher than was calculated there. The reason is that, for numerous reasons, cards are in fact re-issued before they expire. One reason is that, for example, someone upgrades from gold to platinum. Another reason is that people report lost or stolen cards. And the biggest reason is that whenever a merchant is breached, some banks will re-issue en masse to every one who used that merchant.

 

[Steven G]

I could really use help on a problem I cannot solve.

My business accepts credit cards for monthly software subscriptions. One of our biggest challenges is billing failures due to expired credit cards. It "seems" like we have an abnormally high number, but "seems" is meaningless when there is certainly math to help me "know."

So, let's assume:

- Every credit card, when issued, has 36 months before expiration
- We sell a 12-month agreement, and our customers pay by credit card

My question is this: If I sell 100 contracts in January, and January is guaranteed paid (as we know if it went through), what is the probability in each of the following 11 months (February through December) that the credit cards used to sign up in January fail due to expiration?

I hope this is a clear question. And I sincerely appreciate your help.

What percentage are you getting? The answer to your question will be slightly less that 33 1/3%