(32S) Accurate TVM with direct solutions

05172015, 12:55 AM
Post: #1




(32S) Accurate TVM with direct solutions
Total size: 183 bytes
This TVM solver uses direct solutions to compute n, PV, PMT, and FV. Solutions for i% must be obtained using the builtin numeric solver. The multiple direct solutions account for its size, although common expressions have been moved to subroutines where possible. Results are obtained very quickly by using direct solutions. Most of the math in this program is based on discussion in this thread. Usage Store values in appropriate registers: N  n (Number of periods) I  i% (Periodic interest rate, NOT i%/yr) P  PV (Present value) M  PMT (Payment) F  FV (Future value) Set flag 0 for begin period payments, or clear for end period payments. Execute the desired routine to compute the remaining variable: XEQ N  Compute n XEQ I  Compute i% (Periodic interest rate, NOT i%/yr) XEQ P  Compute PV XEQ M  Compute PMT XEQ F  Compute FV Use XEQ V to view/input the TVM variables interactively. Press R/S to cycle through variables. Omit this label if you don't need this feature, and wish to use STO/VIEW directly. Example: 31536000 STO N 10 RCL N / STO I 0 STO P 0.01 CHS STO M CF 0 XEQ F Result: 331,667.006689 Code: V01 LBL V  010.5, 5FF1 

12032015, 12:39 PM
(This post was last modified: 12042015 10:37 PM by PedroLeiva.)
Post: #2




HP 35s  TVM from Gene Wright
Here a TVM program for HP 35s adapated from the original of Gene Wright (1997). It does not calculate interest rate.
Includes program steps, instructions and examples Pedro EDIT: I changed the attachment because a minimum error in the instructions 

12262015, 11:24 PM
(This post was last modified: 12272015 10:35 PM by Jeff_Kearns.)
Post: #3




RE: (32S) Accurate TVM with direct solutions
Dave,
In a previous discussion in March 2014, Thomas Klemm recommended that you follow the links to find a formula in Miguel Toro's post about a program for the HP 35s. Instead of the 13 Label, 122line program you posted, I would recommend this short (extremely ACCURATE) 38 line program that only uses 1 label, which is essentially Miguel Toro's program for the 35s... T001 LBL T T002 INPUT N T003 INPUT I T004 INPUT B T005 INPUT P T006 INPUT F T007 INPUT E T008 RCL I T009 100 T010 / T011 ENTER T012 ENTER T013 1 T014 + T015 LN T016 x<>y T017 LASTx T018 1 T019 X<>Y? !x not equal to y? T020  T021 / T022 * T023 RCL* N T024 e^x T025 RCL* B T026 LASTx T027 1 T028  T029 RCL* P T030 RCL I T031 100 T032 / T033 1/X T034 RCL+ E T035 * T036 + T037 RCL+ F T038 RTN Usage: Select Function (FN= T), then SOLVE for the unknown variable (N, I, B, P, or F). The program prompts for other variables, and E is for Begin/End mode  where E=0 is END MODE. Jeff Kearns 

12302015, 08:22 AM
(This post was last modified: 12302015 08:26 AM by Dieter.)
Post: #4




RE: (32S) Accurate TVM with direct solutions
(12262015 11:24 PM)Jeff_Kearns Wrote: Instead of the 13 Label, 122line program you posted, I would recommend this short (extremely ACCURATE) 38 line program that only uses 1 label, which is essentially Miguel Toro's program for the 35s... Jeff, please take a look at the thread title: it says "Accurate TVM with direct solutions". That's the point here: Except the routine for the interest rate (which cannot be calculated directly) Dave's program returns the results immediately by direct calculation – no solver and no iterations required, and the user also does not have to provide two initial guesses. Maybe the program even is a tiny bit more accurate since it seems to include implementations of both an e^{x}–1 and a ln(1+x) function, while the version you suggested only does the latter. So both versions have their benefits. Yours is very short and compact while Dave's is faster and returns directly calculated results immediately. Dieter 

12302015, 12:13 PM
Post: #5




RE: (32S) Accurate TVM with direct solutions
(12302015 08:22 AM)Dieter Wrote:(12262015 11:24 PM)Jeff_Kearns Wrote: Instead of the 13 Label, 122line program you posted, I would recommend this short (extremely ACCURATE) 38 line program that only uses 1 label, which is essentially Miguel Toro's program for the 35s... Right, this one is built for speed (which is often important when making quick financial decisions). As such, it makes quite a few sacrifices on size. I do have a onelabel solverbased version kicking around for when I only need to run a few numbers, and don't want to type in a large program. Or better yet, I just grab my 17BII. 

12302015, 03:05 PM
(This post was last modified: 12302015 05:11 PM by Jeff_Kearns.)
Post: #6




RE: (32S) Accurate TVM with direct solutions
(12302015 12:13 PM)Dave Britten Wrote:(12302015 08:22 AM)Dieter Wrote: Dave's program returns the results immediately by direct calculation – no solver and no iterations required, and the user also does not have to provide two initial guesses. Gents ~ While I applaud Dave for including his 'direct solutions' program, I have to disagree with a number of statements you each made. First of all, the accuracy of the 38line, singlelabel SOLVER program is on par with that of any financial calculator. It includes both functions (e^(x–1) and ln(1+x)) to which you refer. Just test it with the example in the 15C Advanced Function Handbook, repeated here, or with any other TVM problem. "...and the user also does not have to provide two initial guesses": Believe it or not, this is not (or perhaps seldom) required with the solver program. It works just fine without ever providing initial guesses  except perhaps if one is trying to torture test the program with an extremely high 'N' or a very, very small 'I'. "...Dave's program returns the results immediately": You mean after entering all the variables (unprompted), and looking up which of the routines to execute? If you find waiting a second or two for an answer to a TVM problem, 'on the fly', onerous, then I have no comment. FYI, when solving Dave's example, above  I get the same answer in less than one second. "So both versions have their benefits...Dave's is faster and returns directly calculated results immediately": Dave's 13 label, 122 line program has no practical advantages whatsoever. It is not faster to use at all (especially when you have to set flags...), uses up almost all the available memory, and still requires the solver for interest rate calculations. The calculator has a SOLVER; it is meant to be used! "...I do have a onelabel solverbased version kicking around for when I only need to run a few numbers, and don't want to type in a large program": I think you should type in the 38line program and test it. You will see that it meets all your TVM needs, especially speed and accuracy ;). Jeff 

12312015, 12:23 PM
(This post was last modified: 12312015 01:59 PM by Dieter.)
Post: #7




RE: (32S) Accurate TVM with direct solutions
(12302015 03:05 PM)Jeff_Kearns Wrote: While I applaud Dave for including his 'direct solutions' program, I have to disagree with a number of statements you each made. First of all, the accuracy of the 38line, singlelabel SOLVER program is on par with that of any financial calculator. It includes both functions (e^(x–1) and ln(1+x)) to which you refer. Jeff, I see there is code for a ln(1+x) function (line T008 ff.), but I cannot find something similar for an e^x–1 function (NB: not e^(x1), as you posted). Line T026 ff. simply takes the e^x result and subtracts 1 from it. ;) That's why the solver program will produce errors for very small interest rates. For instance consider this example: N = 10 I = 1E–5 % B = 0 P = 1 E = 0 F = ? Since the interest rate is nearly zero, solving for F correctly returns F=–10,0000045 (i.e. ten times the 1, payment plus with virtually nothing on top because of a nearzero interest rate). Fine. Now replace "I" with 1E–15% and see what you get... The solver will return F=0, which is obviously wrong. This happens because in step T026 the e^x command returns 1 and the following subtraction of 1 yields exactly zero. This is exactly what a dedicated e^x–1 command avoids. "But that's not a real world problem, nobody deals with interest rates that low". Well, the solver program is not able to handle zero interest rates (this causes a division by zero), so using a nearzero interest rate like 1E–20 or 1E–50 is required to handle this case. And here is where the current solver code fails. (12302015 03:05 PM)Jeff_Kearns Wrote: I think you should type in the 38line program and test it. You will see that it meets all your TVM needs, especially speed and accuracy ;). Well... not quite. ;) Addendum: Here is a version that includes both ln(1+x) – using a different method that IHMO performs even better than the original one – as well as an e^x–1 implementation and some slight general improvements. Code: T001 LBL T This code implements this method for ln(1+x) and that one for e^x–1. Dieter 

12312015, 01:37 PM
(This post was last modified: 12312015 02:09 PM by Dave Britten.)
Post: #8




RE: (32S) Accurate TVM with direct solutions
Just for comparison's sake, this is the onelabel solver version that I keep in my pocket 32S notebook "just in case". It's a couple steps longer than Dieter's; I don't know if there are any meaningful differences between the two.
Code:


12312015, 01:49 PM
(This post was last modified: 12312015 01:58 PM by Dieter.)
Post: #9




RE: (32S) Accurate TVM with direct solutions
(12312015 01:37 PM)Dave Britten Wrote: Just for comparison's sake, this is the onelabel solver version that I keep in my pocket 32S notebook "just in case". Are you sure this code is correct? What does the RCL L do – this variable is not used anywhere else. Edit: it seems that L is supposed to hold ln(1+i), but this value is not calculated anywhere in this program. And why don't you just use 100 instead of 2 10^x resp. 200 ÷ instead of 2 10^x ÷ 2 ÷...? ;) Also, there is no need for a temporary register T during the e^x–1 calculation as x/2 is saved in LastX. Dieter 

12312015, 02:04 PM
(This post was last modified: 12312015 02:13 PM by Jeff_Kearns.)
Post: #10




RE: (32S) Accurate TVM with direct solutions
Dieter,
You are correct! I failed to modify the code for the Pioneers after correcting the same mistake in my HP15 code. It now uses using the more accurate e^x1 formula: 2 * sinh(x / 2) * e ^ (x / 2). Corrected 43line code for Accurate TVM in HP32S / HP32sii / HP33s / HP35S T001 LBL T T002 INPUT N T003 INPUT I T004 INPUT B T005 INPUT P T006 INPUT F T007 INPUT E T008 RCL I T009 100 T010 / T011 ENTER T012 ENTER T013 1 T014 + T015 LN T016 x<>y switch x with y T017 LASTx T018 1 T019 X<>Y? x not equal to y? T020  T021 / T022 * T023 RCLx N T024 ENTER T025 e^x T026 RCLx B T027 x<>y T028 2 T029 / T030 SINH T031 LASTx T032 e^x T033 x T034 2 T035 x T036 RCLxP T037 100 T038 RCL/I T039 RCL+E T040 x T041 + T042 RCL+F T043 RTN It now solves correctly for the VVL (very, very, low ;) interest rate example you gave. Regards, Jeff Kearns Dieter wrote: Addendum: Here is a version that includes both ln(1+x) – using a different method that IHMO performs even better than the original one – as well as an e^x–1 implementation and some slight general improvements. I missed that post of yours but presume that my program, being one step shorter than yours, is OK. 

12312015, 02:08 PM
Post: #11




RE: (32S) Accurate TVM with direct solutions
(12312015 01:49 PM)Dieter Wrote:(12312015 01:37 PM)Dave Britten Wrote: Just for comparison's sake, this is the onelabel solver version that I keep in my pocket 32S notebook "just in case". Whoops, I mistranscribed it in my haste. I'll correct it above. The 100 vs. 10^2 thing is a peculiarity of the way the 32S stores numbers. Integers from 099 take up 1.5 bytes. Anything else is 9.5 bytes. So 100 is 9.5 bytes, whereas 2 10^x is only 3 bytes. 

01012016, 02:11 PM
(This post was last modified: 01012016 06:03 PM by Dieter.)
Post: #12




RE: (32S) Accurate TVM with direct solutions
(12312015 02:08 PM)Dave Britten Wrote: Whoops, I mistranscribed it in my haste. I'll correct it above. It still isn't perfect. The ln(1+x) code does not work for very small arguments where 1+x rounds to 1. In this case x+1–1 becomes zero and the following division throws an error. That's why the original (Kahan) code included a x≠y? test.This consumes one more stack level, but it doesn't hurt as the initial calculation of 100/I + B can be done later so this value does not have to be saved on the stack. In general, there is no need for any temporary registers (here T and L), all this can be done on the stack. (12312015 02:08 PM)Dave Britten Wrote: The 100 vs. 10^2 thing is a peculiarity of the way the 32S stores numbers. Integers from 099 take up 1.5 bytes. Anything else is 9.5 bytes. So 100 is 9.5 bytes, whereas 2 10^x is only 3 bytes. I see. But still 10 x^2 is faster than 2 10^x, and there also is a percent function that returns x/100 with a simple 1 %. ;) Edit: I could not believe the 0...99 limit, so I wanted to know what the 32s II manual says. Here is what I found on page 1220/21: "Numbers use 9.5 bytes, except for integer numbers from 0 through 254 which use only 1.5 bytes". There you are: you can safely use "100" and "200" in your program and they still won't require more than 1.5 bytes. Addendum: Here is what I got – I hope there are not too many errors. ;) Code: LBL T At least it's shorter than the previous version (42 lines) and does not require any additional registers. Dieter 

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