HP12c Credit Card Payment Calculation

[vrenaut74]

I've been trying to see if there is a way to input your PMT value, as a percentage of your PV, when calculating for n?

The question I've come across is:

Assume you had a $2,000 balance on your credit card. No further charges are placed on the card, the minimum payment due every month is 2.7%, and the annual interest rate is 18%. How long would it take to pay off the $2,000 balance if you paid the minimum each month?


The input for PMT is what is throwing me off, because I can't just plug in 2.7% of 2000 (54) as the PMT value because that will be wrong once the 1st payment goes through.

I've looked through the manual and online and couldn't find anything, and was just wondering if this wasn't something the HP12c is capable of.

Thanks

[Gamo]

I'm not sure if this credit card payment is similar to amortization.
Here is a link that might help:
https://pocketsense.com/formula-calculat...-3715.html

Gamo

[acapde]

Hi,

I doubt that the built-in TVM function of any business/financial calculator can solve that, at least presented that way.

Being the HP12 a programmable calculator, I would program a loop that calculates each time the payment and the interest added to the capital till the capital is 0 (or less than zero), the number of iterations is the number of periods required to pay the debt off… knowing the credit card companies, it would likely be an infinite loop

This is the way I’d do it, however there might be better ways of achieving it.

Hope it helps.

Andres

[acapde]

(01-25-2018 03:52 AM)Gamo Wrote:  I'm not sure if this credit card payment is similar to armortization.
Here is a link that might help:
https://pocketsense.com/formula-calculat...-3715.html

Gamo

Yes, that might work!

[vrenaut74]

(01-25-2018 03:59 AM)acapde Wrote:  Hi,

I doubt that the built-in TVM function of any business/financial calculator can solve that, at least presented that way.

Being the HP12 a programmable calculator, I would program a loop that calculates each time the payment and the interest added to the capital till the capital is 0 (or less than zero), the number of iterations is the number of periods required to pay the debt off… knowing the credit card companies, it would likely be an infinite loop

This is the way I’d do it, however there might be better ways of achieving it.

Hope it helps.

Andres

Thanks, I'll see if I can figure out a way to do that.

[vrenaut74]

(01-25-2018 03:52 AM)Gamo Wrote:  I'm not sure if this credit card payment is similar to armortization.
Here is a link that might help:
https://pocketsense.com/formula-calculat...-3715.html

Gamo

Thanks, I'm gonna try this

[Carsen]

I wrote a program and I got the answer of 1075 monthly payments. About 89.58 years. My modern 12C screen went blank without the text "running" in the display while running my program (really freaky and weird). It took about 19 seconds to complete the task.

IT IS IMPERATIVE THAT THE [RND] FEATURE IS USED. Because paying 2.7 percent of the current balance every month will never pay off the balance. Unless we round (with RND) to the nearest cent.

Keep in mind that this program is written to solve this problem. I did not design it to tackle a whole bunch of these programs. So it may be inefficient in some areas but my goals is to get the job done.

Code:


01   0
02   RCL  PV
03   f    RND
04   g   X<_Y? (Is X less than or equal to Y conditional test)
05   GTO 00
06   2
07   .
08   7
09   %
10   CHS
11   STO  PMT
12   FV
13   CHS
14   STO  PV
15   1
16   STO + 0
17   GTO 01

Before running the program, make sure REG 0 is empty. Or your answer will be wrong.

Is my solution right? What did everyone else do? What is your solution?

[Dieter]

(01-25-2018 05:11 AM)Carsen Wrote:  IT IS IMPERATIVE THAT THE [RND] FEATURE IS USED. Because paying 2.7 percent of the current balance every month will never pay off the balance. Unless we round (with RND) to the nearest cent.
(...)
Before running the program, make sure REG 0 is empty. Or your answer will be wrong.

Since this is essential for a correct result, why doesn't the program make sure this is observed?
Include a CLX STO 0 and a FIX 2 at the beginning. This adds three steps so that the final GTO 01 becomes GTO 04.

Is the answer supposed to be recalled from R0? Then your program should do this as well, and instead of exiting with a GTO 00 it should jump beyond the last step and do a RCL 0 to display the result.

BTW, I have no idea if this approach is correct since I'm not sure about the original problem. Where do the 18% go in your program? What has to be entered in which way before the program is run? And maybe "vrenaut74" can give a numeric example.

Dieter

[Dieter]

(01-24-2018 08:38 PM)vrenaut74 Wrote:  Assume you had a $2,000 balance on your credit card. No further charges are placed on the card, the minimum payment due every month is 2.7%, and the annual interest rate is 18%. How long would it take to pay off the $2,000 balance if you paid the minimum each month?

I am not sure if I understand this correctly. What does this mean exactly?

So you have $2000 and 2,7% of this is charged, i.e. 2000–54 = $1946 is left after the first month. For this a yearly interest rate of 18% is applied, i.e. 1,5% per month, so $29,19 is added to get $1975,19. Is it like this? Or is the interest added once per year, i.e. after twelve 2,7% charges finally 18% is added to the remaining capital? Please explain.

Dieter

[SlideRule]

(01-24-2018 08:38 PM)vrenaut74 Wrote:  … Assume you had a $2,000 balance on your credit card. No further charges are placed on the card, the minimum payment due every month is 2.7%, and the annual interest rate is 18%. How long would it take to pay off the $2,000 balance if you paid the minimum each month? … and was just wondering if this wasn't something the HP12c is capable of…

As a single calculation, no: as a series of calculations, yes. However, the question is, perhaps, better addressed as a Calculus rather than a Business expression. The question posed seems more academic than practical in so far as the declining minimum payment is (or should be) marginally acceptable or palatable to the debt holder. Is a one cent payment reasonable?

The attached table/graph facilitates this perspective.
[attachment=5593]
This demonstration make some simplifying assumptions but illustrates a valid perspective. Hope this helps.

BEST!
SlideRule

[Dave Britten]

Credit cards don't usually have a straight percentage of the balance as a minimum payment, do they? With my wife's credit card, which we often use for hotel rooms and travel, I think the bill usually just says there's a $35 minimum payment. It might be something like the greater of $35 or some percentage of the balance, unless the balance is less than $35, in which case it's due in full. I'm not really sure, as I haven't scrutinized the terms; we just pay it in full whenever the bill shows up.

In any case, those might be things to consider when developing such a routine.

[Gerson W. Barbosa]

(01-24-2018 08:38 PM)vrenaut74 Wrote:  ...and the annual interest rate is 18%.

Why so low? Here in Wonderland American Express will charge me 446,63% per year if I forget to pay them on time, but only because our annual inflation rate is currently under 3%.

[vrenaut74]

Okay so a little background, because after someone above saying they believe the question is purely academic, I was starting to think they were correct, because a % of the current balance as a minimum payment is something I've never seen.

I'm currently taking a CFP course in order to take the CFP exam, and this was a sample question, when going over debt management. I contacted the course admin and they did agree that this question is purely to get an understanding of how credit APRs and interest rates work, not to use your calculator to solve.

The answer is below:

Quote:The answer is 11 years. More importantly, how much in interest would you have paid the credit card company?

The answer is $1,902.

You would need to amortize this loan as follows:

Interest on first payment is $30 ($2,000 x 18%) / 12 months
Minimum payment is $54 calculated as the beginning balance ($2,000 x 2.7%)
The principal paid on this payment is $24 (the $54 minimum payment - $30 interest)

For the next payment, the balance is $1,976 ($2,000 - $24) of which $53.35 will paid, broken out at as $29.64 of interest [($1,976 x 18%) / 12] and $23.71 as principal ($53.35 - $29.64). You continue this process to obtain the 11 year answer.

[Carsen]

I still do not understand. If you pay 2.7% of the current balance every month, then it will never pay off the balance.

[DavidM]

(01-25-2018 05:55 PM)vrenaut74 Wrote:  The answer is below:

Quote:The answer is 11 years. More importantly, how much in interest would you have paid the credit card company?

The answer is $1,902.

You would need to amortize this loan as follows:

Interest on first payment is $30 ($2,000 x 18%) / 12 months
Minimum payment is $54 calculated as the beginning balance ($2,000 x 2.7%)
The principal paid on this payment is $24 (the $54 minimum payment - $30 interest)

For the next payment, the balance is $1,976 ($2,000 - $24) of which $53.35 will paid, broken out at as $29.64 of interest [($1,976 x 18%) / 12] and $23.71 as principal ($53.35 - $29.64). You continue this process to obtain the 11 year answer.

The amortization described above as "the answer" makes perfect sense to me, but the conclusion does not. To gain a better understanding, I put together a table in Excel that rounds the payment and interest amounts to the nearest cent, then determines the principal amount so that the balance can be adjusted properly for the next payment. Accumulated interest is also included for each period.

The first 5 entries of the resulting amortization schedule that results are shown below. As you can see, the first two lines match the above description:

\begin{array}{|crrrrr|}
\hline
\textbf{Pmt #} & \textbf{Balance} & \textbf{Pmt} & \textbf{Int} & \textbf{Principal} & \textbf{Accum. Int} \\
\hline
1 & 2000.00 & 54.00 & 30.00 & 24.00 & 30.00 \\
2 & 1976.00 & 53.35 & 29.64 & 23.71 & 59.64 \\
3 & 1952.29 & 52.71 & 29.28 & 23.43 & 88.92 \\
4 & 1928.86 & 52.08 & 28.93 & 23.15 & 117.85 \\
5 & 1905.71 & 51.45 & 28.59 & 22.86 & 146.44 \\
... & ... & ... & ... & ... & ... \\
\hline
\end{array}

Carrying this through to the 132nd payment (end of 11th year) gives the following results:

\begin{array}{|crrrrr|}
\hline
\textbf{Pmt #} & \textbf{Balance} & \textbf{Pmt} & \textbf{Int} & \textbf{Principal} & \textbf{Accum. Int} \\
\hline
… & … & … & … & … & … \\
128 & 431.64 & 11.65 & 6.47 & 5.18 & 1966.72 \\
129 & 426.46 & 11.51 & 6.40 & 5.11 & 1973.12 \\
130 & 421.35 & 11.38 & 6.32 & 5.06 & 1979.44 \\
131 & 416.29 & 11.24 & 6.24 & 5.00 & 1985.68 \\
132 & 411.29 & 11.10 & 6.17 & 4.93 & 1991.85 \\
\hline
\end{array}

So it doesn't appear that the balance would have been paid off yet at the time indicated in the answer, and the accumulated interest is higher than specified as well. Furthermore, continued payments of 2.7% of the remaining balance will result in a slowly declining balance that eventually stabilizes at $0.55, at which point the 0.01 payment is fully consumed by the interest due. This results in a balance which will never decline from that point forward, so the credit card balance will never be paid off:

\begin{array}{|crrrrr|}
\hline
\textbf{Pmt #} & \textbf{Balance} & \textbf{Pmt} & \textbf{Int} & \textbf{Principal} & \textbf{Accum. Int} \\
\hline
… & … & … & … & … & … \\
676 & 0.57 & 0.02 & 0.01 & 0.01 & 2498.97 \\
677 & 0.56 & 0.02 & 0.01 & 0.01 & 2498.98 \\
678 & 0.55 & 0.01 & 0.01 & 0.00 & 2498.99 \\
679 & 0.55 & 0.01 & 0.01 & 0.00 & 2499.00 \\
680 & 0.55 & 0.01 & 0.01 & 0.00 & 2499.01 \\
… & … & … & … & … & … \\
\hline
\end{array}

It seems to me that one of the following must be true:

- I am making some huge errors in my interpretation of this problem, or at the very least my implementation of the solution
- There are unstated assumptions or qualifications for the problem that have yet to be disclosed (eg. minimum payment "no less than" some amount)
- The stated answer from the course administrator is in error

I'd be most grateful if someone could clarify what circumstances would make the course administrator's solution match the stated outcome of an 11-year payoff with accumulated interest of $1902. The closest I've come is if I set a minimum payment of 2.7% or $21, whichever is greater.

Has anyone else been able to confirm the administrator's result? I'd appreciate seeing more details about how this problem is supposed to be solved.

[Csaba Tizedes]

OK, first thing: you'll never will pay back that 2000.- USD, because (without interest (18% / year)) you'll pay 2.7%, but always remain 97.3% in every period.

Your real question is: if I can pay (in the future) an affordable PV \( (PV_a) \) in one payment, how many periods I must to pay until \( PV_{actual}<PV_a \)?

This is easy to calculate, because the change of the present value for one period is \( \displaystyle \Delta PV=PV·(d+r) \), where \( d=-0.027 \) and \( r=+0.0139 \) (this is the annual 18% converted to one period = 1.39%).

You can rearrange the above equation: \( \displaystyle \frac{\Delta PV}{PV}=(d+r) \), which is equal \( \displaystyle \frac{1}{PV}·\frac{dPV}{dt}=(d+r) \). Then simply integrate this equation from the initial PV \( (PV_0) \) to affordable PV \( (PV_a) \) and you get the number of periods \( (N) \):

\( \displaystyle \int_{PV_0}^{PV_a} \frac{dPV}{PV} = \int_{0}^{N} d+r \,dt \)

\( \bbox[yellow,5px] { \displaystyle N= \frac {ln \frac{PV_a}{PV_0}}{d+r} } \)

For example, if you can pay in the future 100.- USD \( (PV_a=100) \), then you need pay payments for \( N=228 \) periods, or if \( PV_a=50 \) you will pay for \( N=281 \) periods.

Of course I have checked in EXCEL and OK.

Csaba

[Bill (Smithville NJ)]

(01-25-2018 07:36 PM)Carsen Wrote:  I still do not understand. If you pay 2.7% of the current balance every month, then it will never pay off the balance.

You would need to read the credit card agreement. There would be some statement that says 2.7% of the current balance. If the resultant balance is less than some value (i.e., $10 or $20) then the minimum payment is the resultant balance.

Another item that can come into play is how the interest is calculated. For example, American Express uses either the "daily balance method (including current transactions) (Interest Rate Type D) or the "average daily balance method (including current transactions" (Interest Rate Type A).

To quote:

Daily Balance Method (Type D): "We figure the interest charge by multiplying the daily balance by its periodic rate each day in the billing period. To get a daily balance, we take the balance at the end of the previous day, add the interest on the previous day's balance and new charges, subtract new credits or payments, and make adjustments. The Balance Subject to Interest Rate is the average of the daily balances.

NOTE: I find the Type D description somewhat confusing. It appears to add interest each day on previous balance and then the last statement says "average of the daily balances."

Average Daily Balance Method (Type A): To get an average daily balance, we take the balance at the end of the previous day, add new charges, subtract new credits or payments, and make adjustments. We add all the daily balances and divide by the number of days in the billing period. We figure the interest charge by multiplying the average daily balance by the monthly periodic rate, or by the daily periodic rate and the number of days in the billing period, as applicable.

Another complication is whether your interest rate is fixed or variable based on some index.

Question: Which Method (D or A) is better for the consumer who carries a monthly balance. Or vice versa - which is better for the Credit Card Company?

After typing this, I now have a headache!

Bill
Smithville, NJ

[Gamo]

Look like in the HP-12C Solution Handbook on page 23 got this similar problem called Add-On Rate Loan with Credit Life. Still not sure if this is the same situation but check it out.

Gamo

[gpltaylor]

Hi All, I came across this post on my travels and I wanted to post what I use.

NOTE: This is not within a loop, it's used to proof each iteration of an amortisation calculation. however, adding a loop and storing the agrigates within REGs will not be hard to add.

The following registers need to be assigned before running the program

########## Required REGs#################
# Calc Interest
## I = (Annual Rate / 100 / 12)
## PV = Loan
## 3% STO 1 (REG 1 is the min payment %)

########## REGs Values after Running #########

### Register Afer run
# 7: Interest Payment
# 8: Min Payment
# PV: Current PV after deduction

########## The Program #################
f P/RCL
f PRGM

### Calculate the Interest
RCL PV
RCL I (need to be Annual Rate / 100 / 12)
*
ENTER
STO 7 ## We need this later on to add to the PV

### Calculate the Min Payment
RCL PV
RVL 1
*
STO 8

## Calculate New PV
RCL PV
RCL 7
+
STO PV
RCL PV
RCL 8
-
STO PV

f P/R
g GTO 00

###########
18
100
-
STO i
2000
STO PV
R/S
###

I hope this is useful