Announcement: Calculator Reviews
In the coming weeks, I have acquired a lot of calculators and plan to give a short review of each. They include, the original Hewlett Packard HP 10B, Casio EL5500 III, and the Calculated Industries Construction Pro/Trig App.
Fun with the HP 12C (I lost count on how segments I done so far)
More fun with the HP 12C! (The HP 12C is on my list of top ten calculators of all time  the other nine I have to think about... subject of a future post?). I like using the HP 12C for a variety of applications and not just strictly finance. Here are four more programs, enjoy!
HP 12C:
Rule of 78
When a
mortgage, a loan, a lease, or other annuity is paid early, we can determine how
much interest rebate is due by the Rule of 78:
Rebate = ( (n –
k + 1) * FC ) / ( (n + 1) * n)
Where:
n = the length of
the annuity (number of periods)
k = the period
where the loan is paid off
FC = total
interest, finance charge = PMT * n – PV
The program
will require the user to input and compute the annuity variables [ n ], [ i ],
[ PV ], and [PMT] ([FV] if a balloon payment is required). Then enter the period # where the loan is
paid off (k), and press [R/S].
Program:
Keep in mind:
this is done on the HP 12C (regular).
For the HP 12C Platinum, the code for Last X is 43, 40 ([ g ] [ + ])
STEP

KEY

CODE NUMBER

01

STO 1

44, 1

02

RCL PMT

45, 14

03

RCL n

45, 11

04

*

20

05

RCL PV

45, 13

06

+

40

07

CHS

16

08

STO 0

44, 0

09

RCL n

45, 11

10

RCL 1

45, 1

11



30

12

1

1

13

+

40

14

*

20

15

RCL 1

45, 1

16

÷

10

17

LST x

43, 36

18

1

1

19

+

40

20

÷

10

21

GTO 00

43, 33, 00

Example: On a 48 month purchase of a $20,000 car,
financed at 5%, the purchaser pays the car off early after 24 payments (k =
24). What is the rebate?
Output:
Find the
payment:
[ f ]
[X<>Y] (CLEAR FIN) (if necessary)
48 [ n ]
5 [ g ] [ i ]
(12÷)
20000 [ PV ]
[ PMT ] (payment = 460.59)
24 [R/S]
Rebate: $87.84
Source: Rosenstein, Morton. Computing With the Scientific Calculator Casio: Tokyo, Japan.
1986. ISBN10: 1124161430
HP 12C: Slicing a Right Triangle
The program
finds slices a right triangle into equal parts.
Using similar triangles, the bases and heights of similar triangles are
found.
STEP

KEY

CODE NUMBER

01

RCL 0

45, 0

02

RCL 2

45, 2

03

÷

10

04

INTG

43, 25

05

STO 3

44, 3

06

1

1

07

STO 4

44, 4

08

RCL 0

45, 0

09

RCL 3

45, 3

10

RCL 4

45, 4

11

*

20

12



30

13

R/S

31

14

RCL 1

45, 1

15

*

20

16

RCL 0

45, 0

17

÷

10

18

R/S

31

19

1

1

20

STO+ 4

44, 40, 4

21

RCL 2

45, 2

22

RCL 4

45, 4

23

X≤Y

43, 34

24

GTO 08

43, 33, 08

25

GTO 00

43, 33, 00

Input: Prestore the following values:
Run in Register
0 (R0)
Rise in
Register 1 (R1)
Number of
partitions in Register (R2)
Output: Loop:
Base of the
smaller triangle (x), press [ R/S ]
Height of the
smaller triangle (y), press [ R/S ]
Loop ends after
n pairs
Example: Run = 5
(R0), Height = 3 (R1), Number of Partitions = 5 (R2)
Output:
X

4.00

3.00

2.00

1.00

0.00

Y

2.40

1.80

1.20

0.60

0.00

HP 12C:
Sums of Σx, Σx^2, Σx^3
This program
takes two arguments:
Y: x
X: n (where n=1, n=2, n=3)
If n = 1, the
sum Σ x from 1 to n is calculated
If n = 2, the
sum Σ x^2 from 1 to n is calculated
If n = 3, the
sum Σ x^3 from 1 to n is calculated
If n is not 1,
2, or 3, an error occurs.
Program:
Keep in mind:
this is done on the HP 12C (regular).
For the HP 12C Platinum, the code for Last X is 43, 40 ([ g ] [ + ]) and
the step numbers are three digits (000 instead of 00).
STEP

KEY

CODE NUMBER

01

X<>Y

34

02

STO 1

44, 1

03

X<>Y

34

04

STO 0

44, 0

05

1

1

06



30

07

X=0

43,35

08

GTO 21

44, 33, 21

09

RCL 0

45, 0

10

2

2

11



30

12

X=0

43, 35

13

GTO 29

44, 33, 29

14

RCL 0

45, 0

15

3

3

16



30

17

X=0

43, 35

18

GTO 46

43, 33, 46

19

0

0

20

÷

10

21

RCL 1

45, 1

22

ENTER

36

23

*

20

24

LST X

43, 36

25

+

40

26

2

2

27

÷

10

28

GTO 00

43, 33, 00

29

RCL 1

45, 1

30

ENTER

36

31

*

20

32

LST X

43, 36

33

X<>Y

34

34

3

3

35

*

20

36

+

40

37

RCL 1

45, 1

38

3

3

39

Y^X

21

40

2

2

41

*

20

42

+

40

43

6

6

44

÷

10

45

GTO 00

43, 33, 00

46

RCL 1

45, 1

47

ENTER

36

48

ENTER

36

49

1

1

50

+

40

51

*

20

52

ENTER

36

53

*

20

54

4

4

55

÷

10

56

GTO 00

43, 33, 00

Example: n = 5
Y: 5, X: 1.
Result: 15
Y: 5, X: 2.
Result: 55
Y: 5, X: 3.
Result 225
For an object
that travels in a projectile motion, we can track its range (distance traveled
from the beginning) and height by:
R = v^2 * sin
(2 * θ)/g
H = (v^2 * (sin
θ)^2) / (2 * g)
Where:
v = initial
velocity
θ = initial
angle
g = Earth’s
gravity. For in US units, g = 32.1740468
ft/s^2.
This program
uses the approximation g ≈ 32.174 ft/s^2
The projectile
will have maximum range (distance) if we aim the object at 45°.

Aside: Why?
Let’s let range
(R) be a function of angle (θ):
R = v^2/g *
sin(2 * θ)
Find the
critical points by finding the zero of the first derivative:
dR/dθ = 2 *
v^2/g * cos (2 * θ)
0 = 2 * v^2/g *
cos (2 * θ)
0 = cos (2 * θ)
arccos 0 = 2 * θ
π/2 = 2 * θ
θ = π/4
Now we can use
the second derivative to test whether the function is at a maximum (less than
0) and minimum (more than 0) at the crucial point.
d^2 R/dθ^2 = 4
* v^2/g * sin(2 * θ)
Let θ = π/4
4 * v^2/g *
sin(2 * π/4) = 4 * v^2/g * sin(π/2) = 4 * v^2/g < 0
(We are assuming
the initial velocity is positive, and g ≈ 32.174 >0)
Since the
second derivative at θ = π/4 is negative, the range is at its maximum.
Note that in calculus, angles are measured in radians. π/2 radians in degrees is 90° and π/4 radians in degrees is
45°. (We are only concentrating on
angles between 0° and 90°)

To find the
maximum range and height, substitute at θ = 45° and range and height are:
R = v^2 /g
H = v^2 / (4 *
g)
The time this
certain projectile lasts is:
T = (v * √2) /
(2 * g)
Program:
Keep in mind:
this is done on the HP 12C (regular).
For the HP 12C Platinum, the code for Last X is 43, 40 ([ g ] [ + ])
STEP

KEY

CODE NUMBER

01

STO 1

44, 1

02

2

2

03

÷

10

04

LST x

43, 36

05

√x

43, 21

06

*

20

07

3

3

08

2

2

09

.

48

10

1

1

11

7

7

12

4

4

13

STO 0

44, 0

14

÷

10

15

R/S

31

16

RCL 1

45, 1

17

ENTER

36

18

*

20

19

RCL 0

45, 0

20

÷

10

21

R/S

31

22

4

4

23

÷

10

24

GTO 00

43, 33, 00

Input: velocity in ft/s (convert from mph to ft/s by multiplying it
by 22/15)
Output:
time of
projectile in seconds, [R/S]
range of
projectile in feet, [R/S]
height of
projectile in feet
Example:
V = 25 mph =
36.6666667 ft/s (110/3)
Output:
Time: 0.81 sec,
Range: 41.79 ft, Height: 10.45 ft
Source: Rosenstein, Morton. Computing With the Scientific Calculator Casio: Tokyo, Japan.
1986. ISBN10: 1124161430
Eddie
This blog is property of Edward Shore, 2017. (2017, wow! 7 days already have passed.)
Very useful information and program instructions with HP 12C calculator.
ReplyDeleteKeep the good work !!
Thank you! I love working with the 12C. I wasn't a fan at first (we're talking 20 years ago), but it grew on me. It's one the of the best calculators.
DeleteEddie
Many thanks Eddie once again for a superb article on programming a calculator. Would love to read about your top ten alltimefavorite calculators! I think it would be interesting to see which company's calculators tug at your heart (and head) the most.
ReplyDeleteTI
HP
Casio
Thanks again for all your posts and your incisive videos on YouTube also.
Best wishes.
Joseph
Thank you, Joseph. I have made not made the list yet. I have four definite calculators so far.
DeleteEddie