The Museum of HP Calculators

Loan and Savings on the HP-41C/CV/CX

This program is supplied without representation or warranty of any kind. Auke Hoekstra and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Introduction

In the '80-ties I used my HP-41CX for studies and hobby. Since then I kept it in a save place. Now after about eight years of silence I unintendedly searched on internet for "HP41". This museum site was a place where crazy people like me were still showing interest in old calculators. It is crazy because who runs a program on an HP-41 which can run 1000 times faster on a Pentium laptop. It is fascinating because you try to make a program with the minimum number of lines or the optimal algorithm to use the smallest number of registers or make as much as possible use of the stack registers.

Having started programming on my HP-41CX again, I would like to publish a few of my (old) programs for reasons of reviving the HP-41 feelings again.

I would very much appreciate if you would reply to me on the HP-41 topic.

Overview

The loan and savings program was written to review different ways of managing the mortgage and savings. Most banks can provide you with nice listings but what if the interest changes? Below may help a little. A feeling of nostalgia will be experienced when calculating a mortgage over a period of 30 years. The calculation loop has to be performed 360 times. The cursor has to move 30 times over the display, although replaced by a counter.

The listing below shows an extended command in line 08: ATOX. This is to check whether the input character was an 'L' (value 76). For the C and CV this can be replaced by changing it an ASTO X followed by 'L'. The same applies to line 11 where the compare character is an 'S' (value 83).

The number of bytes can easily be reduced by removing subroutine LBL 06 and its calls XEQ 06 or by deleting lines 01-13.

Usage

Using the loan and savings program is easy. For both calculations you need to enter three parameters.

The LOAN program requires the following parameters:

the Amount to borrow in your own currency
the effective Annual Interest
the Number of Months to pay it back

The outcome will be the Monthly Payment for the loan (mortgage) on the basis of annuity.

The SAVE program requires the following parameters:

the Monthly Payment in your own currency
the effective Annual Interest
the Number of Months to save your money

The SAVE program calculates the final Lump Sum you receive after the period of saving.

Loan Example

Please note that a European setting has been used (flag 28) as well as my default FIX 5 setting.

Keystrokes:               Display:          Comments:
[XEQ][ALPHA] L/S [ALPHA]  L/S?              - Choose loan or savings calculation
L
[R/S]                     AMT=?             - Enter the loan AMOUNT
50000                   
[R/S]                     I%=?              - Enter the annual interest
7,5
[R/S]                     NR.M=?            - Enter the duration in number of months
240
[R/S]                     20                - Count down in years
                          19
                          ..
                          2
                          1
                          M.P=402,80        - Monthly Payment

Savings Example

Keystrokes:               Display:          Comments:
                                            - Continued from previous example
[R/S]                     L/S?              - Choose loan or savings calculation
S
[R/S]                     M.P=?             - Enter the monthly payment
150
[R/S]                     I%=?              - Enter the annual interest
3
[R/S]                     NR.M=?            - Enter the duration in number of months
60
[R/S]                     5                 - Count down in years
                          4
                          .
                          1
                          SUM=9.721,25      - Lump Sum
[CLX]                     9.721,24941       - Normal display

The programs can be executed directly by either:

[XEQ][ALPHA] LOAN [ALPHA]

[XEQ][ALPHA] SAVE [ALPHA]

Program Listing

LINE  KEYS
  01 LBL'L/S'            { main entry }
  02 LBL 00              { byte saving label } 
  03  'L/S?'
  04  AON
  05  PROMPT
  06  AOFF 
  07  76              
  08  ATOX 
  09  X=Y? 
  10  GTO'LOAN'
  11  83
  12  X#Y?
  13  GTO 00
  14 LBL'SAVE'           { SAVE program }
  15  'M.P=?'
  16  XEQ 05 
  17  *   
  18  'NR.M=?'
  19  PROMPT  
  20  STO 03  
  21  CLX     
  22 LBL 02              { Calculate Sum }
  23  XEQ 06
  24  RCL 01
  25  +     
  26  RCL 02
  27  *     
  28  DSE 03
  29  GTO 02
  30  'SUM='
  31  GTO 07
  32 LBL 05              { Get Interest }
  33  PROMPT
  34  STO 01
  35  'I%=?'
  36  PROMPT
  37  1200  
  38  /     
  39  1     
  40  +     
  41  STO 02
  42  FIX 0
  43  CF 29
  44  RTN   
  45 LBL 06              { Count down display }
  46  RCL 03
  47  STO 04
  48  RDN   
  49  12    
  50  ST/ 04 
  51  X<> 04
  52  FRC   
  53  X=0?  
  54  VIEW L
  55  RDN   
  56  RTN   
  57 LBL'LOAN            { LOAN program }
  58  'AMT=?' 
  59  XEQ 05  
  60  'NR.M=?'
  61  PROMPT  
  62  STO 03  
  63  Y^X     
  64  ,       
  65 LBL 03              { Calculate monthly payment }
  66  XEQ 06
  67  RCL 02  
  68  *       
  69  1       
  70  +       
  71  DSE 03  
  72  GTO 03  
  73  /       
  74  *       
  75  'M.P='  
  76 LBL 07              { Display results }
  77  FIX 2   
  78  ARCL X  
  79  FIX 5   
  80  SF 29   
  81  AVIEW   
  82  END
(177 bytes)

Registers

`R01`	Loan Amount or Monthly Payment
`R02`	Annual Interest
`R03`	Duration in Number of Months
`R04`	Work register for year count down

Formulae

Loan calculation on the basis of annuity is calculated by below algorithm in which AMT and MP represent the amount respectively monthly payment:

MP = AMT r^m = AMT r^m

----------------------- -----------------------

r^m-1 + r^m-2 + .. + r + 1 r(r(r(....) + 1) + 1) + 1

Savings calculation is based on below algorithm in which SUM and MP represent the lump sum respectively monthly payment:

SUM = r(r(r(r(...) + MP) + MP) + MP

r expresses the monthly interest derived from the annual interest I% as follows:

r = 1 + I%

--------

12*100

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MP	= AMT	r^m	= AMT	r^m
		-----------------------		-----------------------
		r^m-1 + r^m-2 + .. + r + 1		r(r(r(....) + 1) + 1) + 1