Adapting 'Accurate' TVM routine on HP-15C (and HP-34C) using MISO Technique

[Jeff_Kearns]

EDIT: The following listing has been edited to reflect feedback from forum members and match the listing in the software library here.
This is (was) my first post on the 'new' forum.

I am trying to adapt the Accurate TVM routine for Pioneers to the HP-15C using Karl Schneider's technique for invoking SOLVE with the routine written as a MISO (multiple-input, single-output) function, with indirect addressing. In this case, there are 6 variables (5 knowns). Karl's article can be found here.

Unfortunately I cannot get it to work and I have exhausted my non-programmer's efforts to debug!

My HP-15C adaptation of the code is as follows (apologies for the formatting):

001 f LBL E
002 STO(i)
003 RCL 2
004 EEX
005 2
006 ÷
007 ENTER
008 ENTER
009 1
010 +
011 LN
012 X<>Y
013 LSTx
014 1
015 X≠Y
016 -
017 ÷
018 *
019 RCL * 1
020 e^x
021 ENTER
022 RCL * 3
023 X<>Y
024 1
025 -
026 RCL * 4
027 EEX
028 2
029 RCL ÷ 2
030 RCL + 6
031 *
032 +
033 RCL + 5
034 RTN

When I try solving for the Present Value (or initial balance 'B') with the following values for a 4 year car loan, at 2.9% annual interest, and $ -658.39 monthly payment:

N = 48 STO 1
I = .2417 (2.9% annual) STO 2
B = STO 3 (in this case the variable I want to solve for, so 3 STO I)
P = -658.39 STO 4
F = 0 STO 5
E = 0 STO 6

The answer in register 3, should be B = 29,804.68. Instead I get B = -214,521.14

Can anyone help me troubleshoot this routine? If I can have a MISO solver routine for the TVM equation in my 15C, it will be very useful indeed. Can then leave the financial calc at home.

Regards,

Jeff Kearns (Ottawa)

[Thomas Klemm]

(01-05-2014 01:06 AM)Jeff_Kearns Wrote:  Can anyone help me troubleshoot this routine?

The problem are these two lines:

022 RCL * 3
023 LSTx

The RCL multiplication doesn't change LASTx.

I've changed that to:

021 ENTER
022 RCL * 3
023 X<>Y

In addition to that I also replaced 100 by EEX 2.
Thus saving two instructions:

001 LBL E
002 STO(i)
003 RCL 2
004 EEX
005 2
006 ÷
007 ENTER
008 ENTER
009 1
010 +
011 LN
012 X<>Y
013 LSTx
014 1
015 X≠Y
016 -
017 ÷
018 *
019 RCL * 1
020 e^x
021 ENTER
022 RCL * 3
023 X<>Y
024 1
025 -
026 RCL * 4
027 EEX
028 2
029 RCL ÷ 2
030 RCL + 6
031 *
032 +
033 RCL + 5
034 RTN

Cheers
Thomas

Edit: Lines 027 - 031 could be improved a little as well.

[Jeff_Kearns]

Thomas - Thanks! It now works beautifully.

Quote:The problem are these two lines:

022 RCL * 3
023 LSTx

The RCL multiplication doesn't change LASTx.

I've changed that to:

021 ENTER
022 RCL * 3
023 X<>Y

Why then, does the routine work on Pioneers, but not on the 15C?

In any event - the 15 C is now a fully functional (for most of my needs anyway) financial calculator with plenty of room for other programs.

Jeff K

[Thomas Klemm]

(01-05-2014 02:18 AM)Jeff_Kearns Wrote:  Thomas - Thanks! It now works beautifully.

Glad, I could help.

Quote:Why then, does the routine work on Pioneers, but not on the 15C?

No idea. Maybe they missed to implement that in the 15C and added that behavior later?
I must admit I was rather surprised. I wasn't aware of this difference.

RCL isn't listed here:


Cheers
Thomas

[Jeff_Kearns]

LASTx function in Pioneer models 32sii/33s/35s:

The recall arithmetic sequence * RCL + variable stores x in LASTx and * RCL variable + stores the recalled number in LASTx.

  LSTx_small.jpg (Size: 2.27 KB / Downloads: 416)

Jeff K

[walter b]

Jeff,

The thumbnail you're showing isn't readable. Please improve.

d:-/

[Jeff_Kearns]

Walter,
I tried editing it (it has to be smaller than 200 Kb) but failed. I will try again tomorrow. It is simply the listing from annex B in the 35s manual on LASTx functions. The same list is in the 32sii manual, and presumably the 32s also.

My apologies for the unreadable attachment - it is not even a thumbnail. Will correct...

Regards,

Jeff Kearns

[Thomas Klemm]

(01-05-2014 04:36 AM)Jeff_Kearns Wrote:  The recall arithmetic sequence * RCL + variable stores x in LASTx and * RCL variable + stores the recalled number in LASTx.

I think it should be read as:

The recall arithmetic sequence X RCL + variable stores x in LASTx and X RCL variable + stores the recalled number in LASTx.

HP 35s scientific calculator
user's guide


HP 32SII
RPN Scientific Calculator
Owner’s Manual


It appears somebody tried to improve the manual for the HP 35s and failed.
At least they fixed the typo: riot vs. not

Cheers
Thomas

[Paul Dale]

The 34S stores Last X when doing recall arithmetic operations I think.

Prof Kahan has some insightful things to say about financial calculations in one of his papers. Sorry no reference. He basically gives some really pathological examples which the 12C can do but few others manage.


- Pauli

[Thomas Klemm]

(01-05-2014 06:24 AM)Paul Dale Wrote:  Sorry no reference.

From Mathematics Written in Sand:

A Penny for your Thoughts.
Enter data:
n := 60*60*24*365 = 31,536,000 sec. per year.
i := 10/n = 0.000 000 317 097 9198 % per sec.
PV := 0
PMT := -0.01 = one cent per sec. to the bank.

Calculators            FV displayed
~~~~~~~~~~~            ~~~~~~~~~~~~
27, 92, 37, 38, 12     331,667.0067
15                     331,667.0070


For instance, recalculating i displays this:

Calculators            press [i] and see ...
~~~~~~~~~~~            ~~~~~~~~~~~~~~~~~~
27, 92, 37, 38         0.000 000 317100
12                     0.000 000 31974
15                     0.000 000 317098


Yield from a Risky Investment.
For an investment of -PV := $ 35,000,000 now,
investors are promised n := 100 equal monthly
installments of an amount PMT yet to be agreed
upon, but between $ 640,000 and $ 1,000,000 ,
plus a final payment at the 100th month of
FV := $ 100,000,000 . How does the yield i ,
reckoned in % per month, vary with PMT ?

    PMT        true i %      i on the HP-15C
 ~~~~~~~~~     ~~~~~~~~~     ~~~~~~~~~~~~~~
$  640,000     2.314053      2.314053
   650,000     2.335758      2.335758
   660,000     2.357528      2.357528
   800,000     2.669065      2.669065
 1,000,000     3.135506      3.135506


Cheers
Thomas

[Jeff_Kearns]

Thomas,

Where did you get your figures for the 15C? They do not match my results.

Quote:A Penny for your Thoughts.
Enter data:
n := 60*60*24*365 = 31,536,000 sec. per year.
i := 10/n = 0.000 000 317 097 9198 % per sec.
PV := 0
PMT := -0.01 = one cent per sec. to the bank.

Calculators FV displayed
~~~~~~~~~~~ ~~~~~~~~~~~~
27, 92, 37, 38, 12 331,667.0067
15 331,667.0081

As for the A Penny for your Thoughts example, both the 15C 'Classic' and LE (with the above TVM routine) give FV = 331,667,0070 - accurate to 9 significant digits and off by -0.000 000 090%. By comparison, the 32sii and 35s both give FV= 331,667.0067.

Neither the 15C LE nor the 15C Classic are capable of calculating the i%. The 15C LE flashes 3.015... E 94 and the Classic went on for 20 minutes before I stopped it.

In the case of the Yield from a Risky Investment example, both the 15C LE and Classic models gave the correct true i% (although the correct numbers will flash in the LE display if one does not provide a suitable initial guess for i% in register 2). The 32sii gives the correct result for i% in all cases.

The 'riot' vs 'not' typo in the 32sii manual only seems to have crept in in edition 5. Edition 4 is correct.

Jeff

[Thomas Klemm]

(01-05-2014 04:55 PM)Jeff_Kearns Wrote:  Where did you get your figures for the 15C? They do not match my results.

As for the A Penny for your Thoughts example, both the 15C 'Classic' and LE (with the above TVM routine) give FV = 331,667,0070 - accurate to 9 significant digits and off by -0.000 000 090%. By comparison, the 32sii and 35s both give FV= 331,667.0067.

Agreed: I had for some reason E (register 6) set to 1.

Quote:Neither the 15C LE nor the 15C Classic are capable of calculating the i%. The 15C LE flashes 3.015... E 94 and the Classic went on for 20 minutes before I stopped it.

Did you set I = 2?
I used 3e-7 and 4e-7 as initial guesses and now I get: 3.170979158e-7

Quote:In the case of the Yield from a Risky Investment example, both the 15C LE and Classic models gave the correct true i% (although the correct numbers will flash in the LE display if one does not provide a suitable initial guess for i% in register 2). The 32sii gives the correct result for i% in all cases.

Darn. Here I must have used FV := $ 1,000,000 instead of FV := $ 100,000,000.
Thanks for checking. I'll adjust my post accordingly.

Quote:The 'riot' vs 'not' typo in the 32sii manual only seems to have crept in in edition 5. Edition 4 is correct.

Maybe they had to scan the document and used an OCR-program?

Best regards
Thomas

[Jeff_Kearns]

Now it works! Thanks Thomas.
Jeff

[Thomas Klemm]

You could add this useful program to the General Software Library.
It's difficult to find it in a random thread.

Kind regards
Thomas

[Jeff_Kearns]

I will add it. Interestingly, I was unable to locate the thread using Google: 'accurate tvm 15c site:hpmuseum.org', or any variant thereof. It does show results for other similar routines in the 'old' forum.

Jeff

[Jeff_Kearns]

(01-06-2014 12:27 AM)Thomas Klemm Wrote:  You could add this useful program to the General Software Library.
It's difficult to find it in a random thread.

Kind regards
Thomas

I now have another program to add to the library, thanks to Katie Wasserman: The same TVM program adapted for the HP-34C. Since the 34C does not have Recall Arithmetic, one has to use a workaround as follows:

1) Replace RCL * 1 with
roll-up
STO 7
roll-down
RCL 1
*
RCL 7
roll-down

2) Replace RCL * 3 with
roll-up
STO 7
roll-down
RCL 3
*
RCL 7
roll-down

3) Replace RCL * 4 with
roll-up
STO 7
roll-down
RCL 4
*
RCL 7
roll-down

4) Replace RCL + 6 with
roll-up
STO 7
roll-down
RCL 6
+
RCL 7
roll-down

5) Replace RCL + 5 with
roll-up
STO 7
roll-down
RCL 5
+
RCL 7
roll-down

The above obviously adds 30 lines of code for a total of 66 lines on the 34C, but once you get the program off and running, you feel like Cap't Zener watching "all them blinkin' lights" solve any of the variables in the TVM equation (albeit a little more slowly than the HP-15C LE does... but that's OK)!

Where is Norm anyway??? He may not have much time for finance-types ;-) but he would likely enjoy having this program on his 'calculateur-de-choix'.

Jeff

[Thomas Klemm]

(01-10-2014 02:46 AM)Jeff_Kearns Wrote:  Since the 34C does not have Recall Arithmetic, one has to use a workaround as follows:

1) Replace RCL * 1 with
roll-up
STO 7
roll-down
RCL 1
*
RCL 7
roll-down

You don't have to do that. A simple RCL 1, * will work. The T-register never contains values that we have to save in register 7. Similar in all other cases. But if it adds to the blinking...

Cheers
Thomas

[Jeff_Kearns]

(01-10-2014 05:08 AM)Thomas Klemm Wrote:  You don't have to do that. A simple RCL 1, * will work. The T-register never contains values that we have to save in register 7. Similar in all other cases. But if it adds to the blinking...

You may be correct insofar as the first RCL * 1 substitution is concerned because there are only 2 numbers on the stack, but I tried that with the others and the program doesn't work. There must be some subtle stack lift thing going on that recall arithmetic avoids in the subsequent substitutions.

I have not thoroughly investigated the issue. Have you tried the program with your suggested change; RCL OPERATION nn to RCL nn OPERATION?

Regards,

Jeff

[Dieter]

(01-10-2014 10:50 PM)Jeff_Kearns Wrote:  

(01-10-2014 05:08 AM)Thomas Klemm Wrote:  You don't have to do that. A simple RCL 1, * will work.

...
I have not thoroughly investigated the issue. Have you tried the program with your suggested change; RCL OPERATION nn to RCL nn OPERATION?

Thomas is right. I tried the program on a HP35s, both with and without RCL-arithmetics. There is just one pitfall you have to watch: that's line 021/022 in Thomas' code. Without RCL-arithmetics another ENTER has to be added there:

With RCL-arithmetics:
ENTER
RCL* 3
X<>Y

...and without:
ENTER
ENTER
RCL 3
*
X<>Y

The additional ENTER here is required to save the content of Y.

Otherwise all occurences of RCL-arithmetics indeed can be replaced by a simple RCL n followed by the respective operation.

Dieter

[Jeff_Kearns]

Thanks Dieter. I will test and verify on the 34C and revise the code in the software section accordingly. It will save a number of steps!

Regards,
Jeff