# Credit related formulas

T

#### Tom Jones

Hi,

I have been examining many of the "home user" debt reduction/elimination
software programs and have been incredibly surprised at how simplistic they
are. Very few do *any* type of true data modeling. For instance, many
programs won't even allow you to declare that a credit card's minimum
monthly payment is a percentage of the existing balance for a given period.

I am a software engineer (who *unfortunately* could use a much more robust
debt reduction modeling tool) so my plan is to write one myself. It took me
all of two days to mimic much of the functionality of existing programs.
Yet, I am amazed that no one has applied any type of AI (artificial
intelligence, genetic algorithms, expert-systems, etc.) to this problem.
Attempting to determine a [provably] optimal debt reduction plan can be a
very complex multivariate problem; in most cases it is impossible to
mathematically prove any given solution is *truly* optimal.

I am hoping that the folks that hang around this group can point me to
references for more complex mathematical formulas that are related to credit
based calculations. I am not financial guru but I have taken some pretty
heavy math courses so I'm not afraid of digging in.

I already have references that detail the simple I = PRT stuff... ;-)

The problem that I am currently stuck on is this:

I have a CC that compounds its interest monthly based upon the average daily
balance during that period. The due date for the bill is the 25th of each
month. I can perform the simple stuff like given the principal, APR, and
payment X, determine how long will it take me to pay off the debt (including
the total interest paid).

What if, instead of paying my bill on time, I pay the bill at the
*beginning* of the month, thus the average daily balance for each period
would be less. The end result is that the total interest paid has
decreased. Unfortunately, I haven't been able to find (or derive) any
formula/algorithm that accomplishes this; but the CC companies can obviously
do it. I am quite sure that every new CC company doesn't figure this stuff
out from scratch - there *has* to be existing formulas for these types of
problems.

Any references (the web, text books, etc.) would be greatly appreciated. If
you have any suggestions for my software please let me know.

-TJ

PS: You cannot reply to my email address - if you want talk to me outside of
this newsgroup please post to the group and I will contact you directly.

J

#### John A. Weeks III

Tom Jones said:
The problem that I am currently stuck on is this:

I have a CC that compounds its interest monthly based upon the average daily
balance during that period. The due date for the bill is the 25th of each
month. I can perform the simple stuff like given the principal, APR, and
payment X, determine how long will it take me to pay off the debt (including
the total interest paid).
You are making this way, way, way too difficult.

Debt reduction is easy. There are two methods, A and B. Pick
one and then rock'n'roll.

Method A - sort your debts in order of interest rate. Pay off
the highest interest rate first. When done, use that money to
pay off the next highest interest rate debt. Repeat until all
debts are paid off.

Method B - sort your debts in order of current balance. Pay
off the smallest balance first. When done, use that money to
payy off the next smallest balance debt. Repeat until all
debts are paid off.

Method A minimizes the interest that you pay. Method B takes
advantage of human emotions to get a series of quick victories
to help keep yourself on the program. Method A is for logical
people, method B is for more emotional people.

This debt is costing you big money. It sapps the life-blood
out of poeple. This is serious, and you need to attack the
debt just like you would attack cancer or termites. Given
that, a few pennies difference in paying on the 7th versus
the 24th isn't going to add up to a hill of beans. The real
issue is getting started and stay on target.

-john-

G

#### Gene E. Utterback, EA

John A. Weeks III said:
You are making this way, way, way too difficult.

Debt reduction is easy. There are two methods, A and B. Pick
one and then rock'n'roll.

Method A - sort your debts in order of interest rate. Pay off
the highest interest rate first. When done, use that money to
pay off the next highest interest rate debt. Repeat until all
debts are paid off.

Method B - sort your debts in order of current balance. Pay
off the smallest balance first. When done, use that money to
payy off the next smallest balance debt. Repeat until all
debts are paid off.

Method A minimizes the interest that you pay. Method B takes
advantage of human emotions to get a series of quick victories
to help keep yourself on the program. Method A is for logical
people, method B is for more emotional people.

This debt is costing you big money. It sapps the life-blood
out of poeple. This is serious, and you need to attack the
debt just like you would attack cancer or termites. Given
that, a few pennies difference in paying on the 7th versus
the 24th isn't going to add up to a hill of beans. The real
issue is getting started and stay on target.

-john-

--
====================================================================
John A. Weeks III 952-432-2708 (e-mail address removed)
Newave Communications http://www.johnweeks.com
====================================================================
I couldn't agree with my esteemed colleague, Mr. Weeks, more. Or as my
pappy used to say, when you have to drive a nail, don't get fancy, just hit
it!

Just an FYI - have you checked out Dave Ramsey at daveramsey.com? He is a
big proponent of being debt free and has what he calls the 4 baby steps:
1 - get a \$1,000 emergency fund set aside
2 - cut up and pay off all credit cards - using Method A from above
3 - increase the emergency fund to 3 to 6 months
4 - pay off the house and invest

Good luck
Gene E. Utterback, EA

T

#### Tom Jones

John A. Weeks III said:
You are making this way, way, way too difficult.

Debt reduction is easy. There are two methods, A and B. Pick
one and then rock'n'roll.

Method A - sort your debts in order of interest rate. Pay off
the highest interest rate first. When done, use that money to
pay off the next highest interest rate debt. Repeat until all
debts are paid off.

Method B - sort your debts in order of current balance. Pay
off the smallest balance first. When done, use that money to
payy off the next smallest balance debt. Repeat until all
debts are paid off.

As a fellow engineer (I perused your website, resume, etc.) I am quite sure
you are aware of the bin-packing/knapsack problems (these are classics in
Computer Science). I am also confident that you are familiar with the
problem classifications of NP, NP-Hard, and NP-Complete.

Debt reduction by its very nature, with the exception of the extrememely
simplistic debt load/structures used in your examples, is NP-Hard - it can
be solved in constant time but it is not possible to mathematically prove
that that any given solution is optimal.

Now I realize that in most situations that having such easy to follow
"algorithms" is highly beneficial; they are easy to understand and more
importantly easy to act upon. Yet, in my specific debt load/structure
situation I have been able to drastically reduce my overall interest

The first thing I did was contact every creditor and request the latest
"monthly due-date" that I could. I then pay *every* debt essentially a
month ahead of time. I have also scheduled several "future" balance
transfers to optimize several special offers offered by several of my
creditors. By performing the above plan I will be debt free in 3 years 6
months (my method does *not* shave much time off the total debt repayment
period compared to the methods that you suggested).

**
What it *DOES* do however is reduce the total amount of interest paid to
these debts by just over \$2000 when compared to either of the methods that
you (and most of the world) suggest.
**

If \$2000 is truly your idea of a hill of beans ("a few pennies difference in
paying on the 7th versus the 24th isn't going to add up to a hill of beans),
then I will quite gladly send you an account number where you should feel
free to deposit as many "beans" as you like.

In conclusion, there *are* better ways to optimize debt reduction but most
people do not have the desire, drive, or capacity to follow such convuluted
plans. I am not suggesting that anyone follow my lead; I just would like
people to understand that they have more options than "A" or "B".

And again, if anyone stumbles across any formulas that could help me better
model my original problem I would greatly appreciate their references.

Thank you,
TJ

M

#### MTW

Tom said:
I then pay
*every* debt essentially a month ahead of time.
I'm sure that John, and I, and most everyone else around here
would agree that you will get out of debt FASTER if you pay the
debts off SOONER. There isn't any rocket science to that, and I
would respectfully suggest that no engineering degrees are
required.

However, many people are struggling to manage their cash flow.
And, in those cases, John's advice is "spot on."

MTW

J

#### John A. Weeks III

Tom Jones said:
What it *DOES* do however is reduce the total amount of interest paid to
these debts by just over \$2000 when compared to either of the methods that
you (and most of the world) suggest.
I don't understand how one could save \$2000 just by moving the due
date back one month. You would have to be paying \$2000 in interest
per month to do that, and you are still keeping the debt for the
same amount of time. Something doesn't feel right here. What are
you really doing?
In conclusion, there *are* better ways to optimize debt reduction but most
people do not have the desire, drive, or capacity to follow such convuluted
plans. I am not suggesting that anyone follow my lead; I just would like
people to understand that they have more options than "A" or "B".
You can use balance transfers with any debt reduction method. The
two methods that I gave, A and B, assume that you have done whatever
you can to get the interest rate down, using balance transfers if
they are available.

-john-

S

#### Sgt. Sausage

Debt reduction by its very nature, with the exception of the extrememely
simplistic debt load/structures used in your examples, is NP-Hard - it can
be solved in constant time but it is not possible to mathematically prove
that that any given solution is optimal.
[snip]

Not!

knowledge of mathematics.

The optimal solution: Pay all debt *now*. Don't wait for
monthly due dates. Pay it *now*. No minimum payments.
No monthly payments. No putting X toward Y credit
card. No shifting payments and figuring out who to pay
and when. No "special offers".

Pay *all* debt *immediately*, Q.E.D.

How is this not the *provably optimal* solution?

Didn't take an engineer, or fancy mathematics to figure
that one out.

Of course, coming up with the funds to pay all the
debt immediately is left as homework for the reader <grin>

[snip]

B

Just an FYI - have you checked out Dave Ramsey at daveramsey.com? He is a
big proponent of being debt free and has what he calls the 4 baby steps:
1 - get a \$1,000 emergency fund set aside
2 - cut up and pay off all credit cards - using Method A from above
Just a small aside or two -
(a) Method A vs. B shouldn't make a huge difference, though
if the balances are substantial, then B has the potential
to save you a lot of money.

(b) I'm always wary of "cut up your credit cards".
Definitely pay them off, but if you cannot control
your spending such that simply having a credit card
and paying it off in full each month is not an option,
there's a real discipline problem here that just
cutting them up will probably not solve.

(c) Having and using and paying on time a credit card is
in general a _good_ thing - keeps a recent and up-to-date
credit account on the records and offers valuable
convenience, as well as the ability to engage in
certain transactions (ie. car rentals, buying things
on the 'net, etc). Credit cards are not evil, they
are tools which can be used or abused, just like
most other tools.

(d) that all said, an audit of one's credit cards is
probably a good idea. At the moment, for example,
I've got and Amex and two Visas. All have rewards
programs, but I really ought to dump one of the
Visas, since it's a miles card for which I pay
an annual fee and I just don't need the miles. But
two or three cards is a reasonable number - when
one of my cards was shut off a couple of months due
to somebody stealing the numbers and engaging in
fraudulent transactions, it was very helpful to
have another on hand (I found out about it being
shut down while actually at a register in a store!).
3 - increase the emergency fund to 3 to 6 months
4 - pay off the house and invest
And, of course, 4 is always a topic for endless discussion.
Ie. whether the order ought to be "invest and then pay off
the house" or vice-versa...

J

#### John A. Weeks III

Just a small aside or two -
(a) Method A vs. B shouldn't make a huge difference, though
if the balances are substantial, then B has the potential
to save you a lot of money.
From a mathematical standpoint, method A is superior. The point
that Dave Ramsey makes is that people are not mathematical, but
rather, are emotional. Paying off debt requires a change in habits,
and habits need to be reinforced. Using method B gets you a few
quick victories, which helps reinforce the habit by giving you an
emotional win.
And, of course, 4 is always a topic for endless discussion.
Ie. whether the order ought to be "invest and then pay off
the house" or vice-versa...
Some people are comfortable with debt, others are not. No
amount of investments are really any good if you are unable
to sleep nights and are sweating bullets over your house debt.
If you have a family, you need to provide them a home that is
not at risk before you go out and chase your windmills. A
paid-off home is one that is not at risk. It all depends on
how you are wired, and how much you value this kind of security.

-john-

E

#### Ed Zollars, CPA

John said:
From a mathematical standpoint, method A is superior. The point
that Dave Ramsey makes is that people are not mathematical, but
rather, are emotional. Paying off debt requires a change in habits,
and habits need to be reinforced. Using method B gets you a few
quick victories, which helps reinforce the habit by giving you an
emotional win.
I think we quite often, in discussion groups like this, tend to
forget about the importance of such emotional factors. While B may
be easily demonstrated to be the preferable mathematical option, A
is clearly superior to doing nothing--and it may very well be that
this is the *true* option on the table if there aren't some
immediate "victories" for most people.

M

#### MTW

While
B may be easily demonstrated to be the preferable mathematical
option, A is clearly superior to doing nothing
OK, pardon my mathematical ignorance, but could you post an
example as to how "B" would be superior?

(Keep in mind, I became a TAX accountant (rather than an
ACCOUNTANT accountant) because I don't understand numbers. <g>)

MTW

B

MTW said:
OK, pardon my mathematical ignorance, but could you post an
example as to how "B" would be superior?
Just to clarify things, *I* misstyped:
[original:]
Method A - sort your debts in order of interest rate. Pay off
Method B - sort your debts in order of current balance. Pay [me:]
Just a small aside or two -
(a) Method A vs. B shouldn't make a huge difference, though
if the balances are substantial, then B has the potential
to save you a lot of money.
Method B _never_ will save you money on interest. Method A
has the potential to save one a lot of money.

The only ways by which I can figure that B can be
superior are these:
(1) psychologically - small wins keeping person to program
(2) other fees _besides_ interest - ie. annual account fees which
go away when zeroed-out accounts close; (other fees?)
(3) one less bill to manage - increasing likelihood of keeping
up with bills in general, decreasing likelihood of missing
a payment - which would lead, again, to more fees.

If interest rates are close, these factors for (B) might
be worthwhile. If they are not - ie. one card is charging
18% and another is charging, say, 9%, jeez, pay off the 18%
first or at least look into transferring the balance or
something.

M

#### MTW

Just to clarify things, *I* misstyped:
OK said:
Method B _never_ will save you money on interest. Method A
has the potential to save one a lot of money.
That's what I've always thought.

MTW