AAoA and Amex Backdating help

[Bay_Area_Joe]

I know this should be simple, but I want to make sure I really understand.

Right now I have 9 total cards with various open dates and resulting ages.  Based on getting several cards in 2012 my AAoA has taken a dip and sits at about 1.8 years.  Which is not very long at all.

I just got my AMEX green on 1-4-2013, but with backing to 1991, I do not know the month so I will guess for math purposes Jan 1991 and to make is simple.

So, with 1.8 years average account and 9 accounts.

Now 10 accounts and I add 21 years to the 1.8 for 22.8/10 = 2.28 AAoA ?

If I add another AMEX account with another 21 years = 2.28+21=23.28/11=2.1 AAoA ?

I just don't understand.

Can somebody put it in simple math for me?

Thank you

[Walt_K]

(1.8*9 + 21)/10 = 3.72

That's assuming you have no other tradelines.  You said nine cards.  If you have installment loans you count those too.

[bs6054]

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@Bay_Area_Joe wrote:

I know this should be simple, but I want to make sure I really understand.

Right now I have 9 total cards with various open dates and resulting ages.  Based on getting several cards in 2012 my AAoA has taken a dip and sits at about 1.8 years.  Which is not very long at all.

I just got my AMEX green on 1-4-2013, but with backing to 1991, I do not know the month so I will guess for math purposes Jan 1991 and to make is simple.

So, with 1.8 years average account and 9 accounts.

Now 10 accounts and I add 21 years to the 1.8 for 22.8/10 = 2.28 AAoA ?

If I add another AMEX account with another 21 years = 2.28+21=23.28/11=2.1 AAoA ?

I just don't understand.

Can somebody put it in simple math for me?

Thank you

---

Did this somewhere else today....  OK, so AAoA, remember what average means.  So if you have 9 accounts with an average of 1.8, that means your current total is 9*1.8=16.2  Your new card adds 21 years, so your new total is 37.2.   You now have ten cards so AAoA = 3.72 years so a fairly big jump.

But, AAoA also counts closed accounts on your report.  Is it 9 open or 9 total

EDIT: Walk_K got there first, fortunately we have the same result!

[Bay_Area_Joe]

Thank you.

I love it.  Two different ways explained and shown but same result.

Thank you.

I am thinking one more AMEX soon and I will get another bump and be sitting pretty good.

I have read before there is point of diminishing return though.

[bs6054]

Well, the calculation was exactly the same, just laid out in a different format.   But for posterity:

Let: A= current AAoA, N = number of accounts (open and closed reporting), B be the # of years you can backdate the new card.

Then

New AAoA= (A*N + B)/(N+1)

As N gets very large, as you would expect this approximates A.  Similarly if A is already large, backdating doesn't make much difference.

Difference of new - old  = (A*N+B)/(N+1) - A

= (A*N+B -A*N-A)/(N+1) =

(B-A)/(N+1)

which is small if N is large or B nearly = A.

[jake619]

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@bs6054 wrote:

Well, the calculation was exactly the same, just laid out in a different format.   But for posterity:

Let: A= current AAoA, N = number of accounts (open and closed reporting), B be the # of years you can backdate the new card.

Then

New AAoA= (A*N + B)/(N+1)

As N gets very large, as you would expect this approximates A.  Similarly if A is already large, backdating doesn't make much difference.

Difference of new - old  = (A*N+B)/(N+1) - A

= (A*N+B -A*N-A)/(N+1) =

(B-A)/(N+1)

which is small if N is large or B nearly = A.

---

Yep, you did this on my post earlier today.  I still can't get my head around the math you put forth.

To me AAoA means:  ((sum of all reporting months / number accounts reporting) / 12) = average

or

((months / accounts) / 12) = average

or

acct A 12 months

acct B 36 months

((48 / 2) / 12) = 2 years

[Walt_K]

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@jake619 wrote:

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@bs6054 wrote:

Well, the calculation was exactly the same, just laid out in a different format.   But for posterity:

Let: A= current AAoA, N = number of accounts (open and closed reporting), B be the # of years you can backdate the new card.

Then

New AAoA= (A*N + B)/(N+1)

As N gets very large, as you would expect this approximates A.  Similarly if A is already large, backdating doesn't make much difference.

Difference of new - old  = (A*N+B)/(N+1) - A

= (A*N+B -A*N-A)/(N+1) =

(B-A)/(N+1)

which is small if N is large or B nearly = A.

---

Yep, you did this on my post earlier today.  I still can't get my head around the math you put forth.

To me AAoA means:  ((sum of all reporting months / number accounts reporting) / 12) = average

or

((months / accounts) / 12) = average

or

acct A 12 months

acct B 36 months

((48 / 2) / 12) = 2 years

---

You're both saying the same thing.  You're just expressing it slightly differently.  You're summing the months of each account to get total account age.  If you don't want to add up all the months/years across your various accounts, and you know your current average, and you also know the number of accounts reporting, you can quickly calculate your total account age by simply multiplying the average by the number of accounts reporting. 

ETA:  Just to clarify, if that didn't help.  If you tell me you have an AAoA of 10 years and you have 5 accounts, I don't need to know whether you have 4 1-yr-old accounts and 1 46-yr-old account or 5 10-yr-old accounts or any other combination.  Because average = total account age/number of accounts, I just multiply number of accounts by average to get total account age.  It's 5*10yrs or 50 years no matter how it is distributed among the individual accounts. 

Then you have to add in the age of the new account for the new total age, and then divide by the new total number of accounts, which is one more account.  In this example, if the person is adding a 21 year old account, it would be (5*10 + 21)/11.  This all assumes you have the current average and number of accounts.  If you're just looking at your report and don't have a current AAoA, you'd have to do it the long way and add up the account age of your individual accounts.

[bs6054]

Right, just using the definition, if you have Number of things, and adding up the values gives Sum,

Average (mean) = Sum/Number

or rearranging, Sum = Average*Number.

This sort of calculation comes up in SAT-type things "John is taking 4 [equally-weighted] exams. He got an average of 87% on the first three.  What score does he need in the 4th exam to get an overall mark of 90%?"