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 Î£x, Î£x^2, Î£x^3
This program
takes two arguments:
Y: x
X: n (where n=1, n=2, n=3)
If n = 1, the
sum Î£ x from 1 to n is calculated
If n = 2, the
sum Î£ x^2 from 1 to n is calculated
If n = 3, the
sum Î£ 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 * Î¸)/g
H = (v^2 * (sin
Î¸)^2) / (2 * g)
Where:
v = initial
velocity
Î¸ = 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 (Î¸):
R = v^2/g *
sin(2 * Î¸)
Find the
critical points by finding the zero of the first derivative:
dR/dÎ¸ = 2 *
v^2/g * cos (2 * Î¸)
0 = 2 * v^2/g *
cos (2 * Î¸)
0 = cos (2 * Î¸)
arccos 0 = 2 * Î¸
Ï€/2 = 2 * Î¸
Î¸ = Ï€/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/dÎ¸^2 = 4
* v^2/g * sin(2 * Î¸)
Let Î¸ = Ï€/4
4 * v^2/g *
sin(2 * Ï€/4) = 4 * v^2/g * sin(Ï€/2) = 4 * v^2/g < 0
(We are assuming
the initial velocity is positive, and g ≈ 32.174 >0)
Since the
second derivative at Î¸ = Ï€/4 is negative, the range is at its maximum.
Note that in calculus, angles are measured in radians. Ï€/2 radians in degrees is 90° and Ï€/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 Î¸ = 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.)