The following warnings occurred:
Warning [2] Undefined array key 41857 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 41878 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 41934 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 41937 - Line: 275 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 275 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $thread - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $fid - Line: 295 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 295 errorHandler->error_callback
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 41878 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined array key 41937 - Line: 331 - File: inc/plugins/threaded_mode.php PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php 331 errorHandler->error_callback
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 332 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 304 ThreadedMode::buildtree
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $theme - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Trying to access array offset on value of type null - Line: 3 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 3 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Undefined variable $lang - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks
Warning [2] Attempt to read property "messages_in_thread" on null - Line: 5 - File: inc/plugins/threaded_mode.php(305) : eval()'d code PHP 8.1.2-1ubuntu2.14 (Linux)
File Line Function
/inc/class_error.php 153 errorHandler->error
/inc/plugins/threaded_mode.php(305) : eval()'d code 5 errorHandler->error_callback
/inc/plugins/threaded_mode.php 305 eval
/inc/plugins/threaded_mode.php 23 ThreadedMode::showthread_threaded
/inc/class_plugins.php 142 threaded_mode_showthread_threaded
/showthread.php 918 pluginSystem->run_hooks





TVM accuracy revisited



#5

Heylo!
Was looking for a good TVM program for my HP41CX and found the improved FI (FIN) program in PPC Journal 1983 Jan/Feb, p.22f. Great program btw :)

In another thread, the first accuracy problem presented in the PPC article was discussed. What is really the most "correct" answer here???

According to the PPC article, the HP12C in those days returned FV=-1,244,458.491 (in the previous thread, the incorrect FV=-1,237,786.903 is mentioned for 12C/P, but the payment period is BEGIN, not END).

The PPC article goes on to calculate the trouble-some interest rate using the super accurate function
(((1+i)^n)-1)/i, where n can be fractional (available on e.g. HP-37E in those days, but not 12C or HP41). This will give FV=-1,244,458.519.

(The above function do exist in 12C, but only works with INT(n). What about 12CP?)

The improved FI (FIN) program for HP41 presented in the article, will give FV=-1,244,458.520, using the accurate E^X-1 and LN1+X functions available on the HP41.

Interestingly, my HP49G emulator (ROM version 1.18) returns FV=-1,244,458.523.

Do we have 10 significant digits here somewhere for FV?

  • HP12C : -1,244,458.491
  • HP41C : -1,244,458.520
  • HP37E : -1,244,458.519 (returns same as 12C in normal use)
  • HP49G : -1,244,458.523

#6

And which would be the correct answer?

#7

Tommi says:

"Do we have 10 significant digits here somewhere for FV?

HP12C : -1,244,458.491

HP41C : -1,244,458.520

HP37E : -1,244,458.519 (returns same as 12C in normal use)

HP49G : -1,244,458.523"

The interest rate in this problem is (lots of digits):

i=.538 993 302 623 106 141 922

The FV is (lots of digits):

FV=-1,244,458.519 105 488 899 859 678

Interestingly, if one computes the interest rate with the following sequence on the HP17B II

(or some similarly Saturn based financial calc)

(begin mode) 1 N 15 I%YR 100 PV FV 26 N I%YR

one gets i=.538 993 302 622

But if one uses the LNP1 and EXPM1 functions on the HP48

and evaluates EXPM1(LN(1.15)/26) one gets:

.538 993 302 623

I'm sure one of the things the later financial calcs, especially the Saturn based ones, did to improve accuracy is to use an internal LNP1 and EXPM1 where appropriate. So why the discrepancy in the LSD?

If this problem is solved with the HP48's TVM solver, and the interest rate is calculated with the keystroke sequence:

(begin mode) 1 N 15 I%YR 100 PV FV 26 N I%YR

the result is -1,244,458.51909

But if the interest rate is calculated as EXPM1(LN(1.15)/26), and this is stored in I%YR, and the FV is solved for,

the result is: -1,244,458.5191, which is more nearly correct . I hadn't before seen a result where the internal result of a Saturn based financial calc is less accurate than what I can calculate myself with the LNP1 and EXPM1 functions.


#8

In the interest of clarity, in my previous posting, where I said:

If this problem is solved with the HP48's TVM solver, and the interest rate is calculated with the keystroke sequence:

(begin mode) 1 N 15 I%YR 100 PV FV 26 N I%YR

the result is -1,244,458.51909

Replace with:

If this problem is solved with the HP48's TVM solver, and the interest rate is calculated with the keystroke sequence:

(begin mode) 1 P/YR 1 N 15 I%YR 100 PV FV 26 N I%YR

Then type 1040 N 0 PV 25 PMT FV

the result is -1,244,458.51909


Possibly Related Threads…
Thread Author Replies Views Last Post
  17BII & 17BII+ Discounted Payback Period Revisited Tom Neudorfl 8 2,809 11-25-2013, 10:28 AM
Last Post: Don Shepherd
  Touch periodic table on HP Prime - revisited Terje Vallestad 2 1,385 11-23-2013, 11:47 AM
Last Post: Mic
  TVM again ;-) fhub 17 4,760 09-02-2013, 11:03 AM
Last Post: fhub
  How much accuracy does one actually need? Matt Agajanian 23 5,575 08-26-2013, 12:46 PM
Last Post: Kimberly Thompson
  TVM WP34s trouble Jim P 4 1,725 06-28-2013, 07:31 AM
Last Post: fhub
  A slide rule to conquer the moon revisited Palmer O. Hanson, Jr. 12 3,501 06-19-2013, 03:05 PM
Last Post: Ken Shaw
  HEPAX Revisited: Revision 1E available Ángel Martin 4 1,569 05-03-2013, 01:57 PM
Last Post: Diego Diaz
  Estimating accuracy in finite precision computations mpi 17 4,245 02-22-2013, 09:44 AM
Last Post: mpi
  TVM-Solver for the PC fhub 14 3,880 12-26-2012, 03:24 PM
Last Post: fhub
  [WP34s] New TVM-solver version fhub 43 10,586 12-26-2012, 06:12 AM
Last Post: fhub

Forum Jump: