HP 12C Using TVM variables as Registers
Special Thanks
Regarding the HP 12C Tips talk I gave on HHC 2017, I received this tip from an email from SergioSamy. Appreciation and gratitude.
To watch my HP 12C tip presentation, click here:
https://www.youtube.com/watch?v=Q54UbDzpAIw
Why Use TVM Variables?
Normally, we use the variables n, i, PV, PMT, and FV for time value of money, cash flow, and depreciation calculations. They can be used for variables for non-finance or other business calculations as well.
When we program on the Classic HP 12C, we have 99 steps. If the program memory is clear, we have 20 registers from R.9 (register dot-nine) to R0 (register zero). For every eight steps, a memory register is lost.
At full capacity of the Classic HP 12C, we only have seven registers left (R0 through R6).
The moment that we use press the [ Σ+ ] button and use statistics, the registers R1 and R6 get occupied, possibly leaving R0 to use for other purposes:
R1 = n
R2 = Σx
R3 = Σx^2
R4 = Σy
R5 = Σy^2
R6 = Σxy
However, the TVM registers: n, i, PV, PMT, and FV, are permanent memory registers for use. Today's programs will illustrate this use.
Note: Pressing the TVM keys once after a number (key word: after) stores the number in a variable. If you don't key a number first, then the program solves for the a variable. Let's look at a couple of examples.
Economic Ordering Quantity
Formula:
EOQ = √(2 * CPO * SLS ÷ (CPU * HOLD%))
CPO = fixed order cost
SLS = number of project sales units
CPU = variable cost per unit
HOLD% = projected cost of holding inventory
EOQ = economic ordering quantity, in units
TVM variables used:
[ n ]: EOQ, computed
[ i ]: HOLD%, entered
[ PV ]: CPU, entered
[ PMT ]: CPO, entered
[ FV ]: SLS, entered
Program Code:
Line Number: Key Code; Key
01: 45, 14; RCL PMT
02: 45, 15; RCL FV
03: 20; ×
04: 2; 2
05: 20; ×
06: 45, 13; RCL PV
07: 45, 12; RCL i
08: 25; %
09: 34; x<>y
10: 33; R↓
11: 10; ÷
12: 43, 21; √
13: 44, 11; STO n
14: 43,33,00; GTO 00
Example
CPO = 40.95
SLS = 8,000
CPU = 5.50
HOLD% = 10%
10 [ i ]
5.50 [ PV ]
40.95 [ PMT ]
8000 [ FV ]
[ R/S ]. Result: 1091.45
Source
HP-17B, HP-19B, HP-27S Step-by-Step Solutions For Your HP Calculator. Marketing and Sales. Hewlett Packard. Edition 1. January 1988
Quadratic Equation
Instructions:
Find the roots of a*x^2 + b*x + c = 0
The program ends with the discriminant stored in R0.
D = b^2 - 4*a*c
If D<0, the roots are complex in the form of s ± ti:
s: real part, stored in PMT
t: imaginary part, stored in FV
If D≥0, the roots are real and:
Root 1 is stored in PMT
Root 2 is stored in FV
Store a in [ n ], b in [ i ], and c [ PV ]. Then run the program.
Note: to get the absolute value, square then take the square root of the number. This is why I have two square root commands in a row: one is to make the absolute value; the second to take the square root of D.
Program Code:
Line Number: Key Code; Key
01: 45,12; RCL I
02: 2; 2
03: 21; y^x
04: 45, 13; RCL PV
05: 45, 11; RCL n
06: 20; ×
07: 4; 4
08: 20; ×
09: 30; -
10: 44, 0; STO 0
11: 45, 12; RCL i
12: 16; CHS
13: 2; 2
14: 10; ÷
15: 45, 11; RCL n
16: 10; ÷
17: 44, 14; STO PMT
18: 45, 0; RCL 0
19: 2; 2
20: 21; y^x
21: 43, 21; √
22: 43, 21; √
23: 2; 2
24: 10; ÷
25: 45, 11; RCL n
26: 10; ÷
27: 44, 15; STO FV
28: 0; 0
29: 45, 0; RCL 0
30: 43, 34; x≤y
31: 43,33,00; GTO 00
32: 45,14; RCL PMT
33: 36; ENTER
34: 36; ENTER
35: 45, 15; RCL FV
36: 30; -
37: 44, 15; RCL FV
38: 33; R↓
39: 43, 36; LSTx
40: 40; +
41: 44,14; STO PMT
42: 45, 0; RCL 0
43: 43,33,00; GTO 00
Examples
2*x^2 - 3*x + 6 = 0
2 [ n ]
-3 [ i ]
6 [ PV ]
[ R/S ]
Results:
D = -39.00 (complex roots)
[ RCL ] [ PMT ]: Real part: 0.75
[ RCL ] [ FV ]: Imaginary part: 1.56
0.75 ± 1.56i
x^2 + 8*x - 4 = 0
1 [ n ]
8 [ i ]
-4 [ PV ]
[ R/S ]
Results:
D = 80
[ RCL ] [ PMT ]: Root 1: 0.47
[ RCL ] [ FV ]: Root 2: -8.47
0.47, -8.47
Hope you find this tip helpful,
Eddie
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