HP Prime: Curve Fitting to Approximate the Zeta Function

HP Prime:  Curve Fitting to Approximate the Zeta Function

Introduction

Here are three approximations for the zeta functions for the positive real numbers x.  For the test data, I used the interval 2 ≤ x ≤ 12.   

For the even integers, exact values are given, otherwise decimal approximations are given.

2,  ζ(2) = π^2 / 6

3,  ζ(3) ≈ 1.202056903

4,  ζ(4) = π^4 / 90

5,  ζ(5) ≈ 1.036927755

6,  ζ(6) = π^6 / 945

7,  ζ(7) ≈ 1.008349277

8,  ζ(8) = π^8 / 9450

9,  ζ(9) ≈ 1.002008392

10,  ζ(10) = π^10 / 93555

11,  ζ(11) ≈ 1.000494189

12,  ζ(12) = 691 * π^12 / 638512875

For x → ∞, ζ → 1

Here are results from three curve fits.  I have tried to include curve fits of at least 10^-2.

Inverse Regression:  Y = A / X + B

Y = 1.42232589936/X+0.81893671619

Average Absolute Error:  5.49240669397ᴇ−2

Logistic Regression:  Y = A / (1 - B * (e^(C * X))

Y = 1.00164385688/(1-2.09727867903*e^(-0.839946048322*X))

Average Absolute Error:  1.41745186091ᴇ−3

Custom Regression:  Y = A + B / X + C X + D X^2

Y = -0.269041227527+(3.20690850188/X)+0.163810293025*X-6.77810226165ᴇ−3*X^2

Average Absolute Error:  1.05418780589ᴇ−2

HP Prime Program:

EXPORT zetamatrix()

BEGIN

LOCAL R,C;

M1:=MAKEMAT(1,11,4);

M2:=MAKEMAT(approx(CAS.Zeta(I+1)),11,1);

FOR R FROM 1 TO 11 DO

M1(R,2):=approx(1/(R+1));

M1(R,3):=approx(R+1);

M1(R,4):=approx((R+1)^2);

END;

END;

Coming up:  Python Week:  August 1 to August 5, 2022

Next Post:  August 2, 2022

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP 32SII Applications: Moments of Inertia, Conductor Temperature Change, Slit Patterns

HP 32SII Applications: Moments of Inertia, Conductor Temperature Change, Slit Patterns

Moment of Inertia - Uniform Disk

The moment of inertia on a uniform disk of radius r is:

I = 2 * π * L * ρ * ∫(r^3 dr, 0, R) 

where ρ = M ÷ ( π * R^2 * L)

The formula of inertia for the uniform disk can be simplified to:

I = M * R^2 * 1/2

where

M = mass of the disk

R = radius of the disk

I = inertia of the center of the mass

HP 32SII Program:

I01  LBL I

I02  INPUT M

I03  INPUT R

I04  x^2

I05  ×

I06  2

I07  ÷

I08  RTN

(12.0 bytes, CK = B55F)

Example:

 

Inputs:

M = 8 kg

R = 0.2 m

Result:

I = 0.16 kg * m^2

Source:

Texas Instruments Incorporated.  Texas Instruments TI-55III Scientific Calculator Sourcebook  Second Edition.  1984

Conductor Temperature Change

The temperature change due to the change of the resistance can be calculated as:

∆t = 1 ÷ α * ( R_2 ÷ R_1 - 1)

where:

∆t = change of temperature in °C

R_2 = new resistance in Ω  (R)

R_1 = new resistance in Ω  (F)

α = temperature coefficient of resistance (A)  (see table below and source)

Selected Temperature Coefficients of Resistance at 20°C (α):

Material:  α

Nickel:  0.005866

Iron:  0.005671

Aluminum:  0.004308

Copper:  0.004041

Silver:  0.003819

Gold:  0.003715

Alloy Steel (99.% iron):  0.003

HP 32SII Program:

T01  LBL T

T02  INPUT A

T03  INPUT R

T04  INPUT F

T05  ÷

T06  1

T07  -

T08  x<>y

T09  1/x

T10  ×

T11 RTN

(16.5 bytes, CK = DDA9)

Example:

Inputs:

A = 0.004041  (α, Copper)

R = 58 Ω  (new resistance)

F = 50 Ω  (old resistance)

Result:

39.594160 °C

Sources:

"Temperature Coefficient of Resistance"  All About Circuits.  Last Retrieved May 17, 2022.  https://www.allaboutcircuits.com/textbook/direct-current/chpt-12/temperature-coefficient-resistance/#:~:text=The%20resistance%2Dchange%20factor%20per,with%20an%20increase%20in%20temperature.

National Radio Institute Alumni Association  Mathematics For Radiotricians Washington, D.C.  1942

Slit Patterns

The intensity of diffraction pattern of the single slit can be calculated by the formula:

I = Im * (sin α ÷ α)^2

where:

Im = potential maximum intensity

α = (π * s * sin θ ÷ λ) in radians

s = slit width

λ = wavelength in Hz

θ = angle of diffraction in degrees

For a double slit:

I = Im * (cos B)^2 * (sin α ÷ α)^2

where:

B is in radians and

B = (π * d * sin θ ÷ λ)

d = distance between slits

θ = angle of diffraction in degrees

α = see the single slit formula above

HP 32SII:

A:  θ

S:  slit wdith

W:  wavelength, λ

I:  maximum intensity

LBL S: single slit

LBL D: double slit, uses LBL S

HP 32SII Programs:

Single Slit:

S01  LBL S

S02  DEG

S03  INPUT A

S04  SIN

S05  INPUT S

S06  ×

S07  π

S08  ×

S09  INPUT W

S10  ÷

S11  RAD

S12  ENTER

S13  SIN

S14  x<>y

S15  ÷

S16  x^2

S17  INPUT I

S18  ×

S19  RTN

(28.5 bytes, CK = 40E0)

Double Slit:

D01  LBL D

D02  XEQ S

D03  DEG

D04  RCL A

D05  SIN

D06  INPUT D

D07  ×

D08  π

D09  ×

D10  RCL÷ W

D11  RAD

D12  COS

D13  x^2

D14  ×

D15  RTN

(22.5 bytes, CK = 8BC7)

Example:

Inputs:

A = 8°

S = 1.96E-6 m

W = 500E-9Hz

I  = 1

Single Slit Calculation:

XEQ S:  0.333496

Double Slit Calculation:

XEQ D

D = 3E-5 m

Result:  0.068409

Source:

Saul, Ken.  The Physics Collection:  Ten HP-41C Programs for First-Year Physics Class  Corvallis, OR.  1986

Coming up:  Python Week:  August 1 to August 5, 2022

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

TI-58/TI-59 Week: Law of Cosines

TI-58/TI-59 Week:  Law of Cosines

Introduction

[ A ]:  stores either the angle θ or a 

[ B ]:  stores the length of side b

[ C ]:  stores the length of side c

[ D ]:  calculates the length of side a:

a^2 = b^2 + c^2 - 2 * b * c * cos θ

[ E ]:  calculates the angle θ

cos θ = (b^2 + c^2 - a^2) / (2 * b * c)

The angle θ is opposite slot of side a.

Program Listing

000 76 LBL

001 11 A

002 42 STO 

003 01 01

004 92 INV SBR (RTN)

005 76 LBL

006 12 B

007 42 STO

008 02 02

009 92 INV SBR

010 76 LBL

011 13 C

012 42 STO

013 03 03

014 92 INV SBR

015 76 LBL

016 14 D

017 43 RCL

018 02 02

019 33 x^2

020 85 +

021 43 RCL

022 03 03

023 33 x^2

024 75 -

025 02 2

026 65 ×

027 43 RCL

028 02 02

029 65 ×

030 43 RCL

031 03 03

032 65 ×

033 43 RCL

034 01 01

035 39 cos

036 95 =

037 34 √

038 42 STO 

039 04 04

040 INV SBR

041 76 LBL

042 15 E

043 53 (

044 43 RCL

045 02 02

046 33 x^2

047 85 +

048 43 RCL

049 03 03

050 33 x^2

051 75 -

052 43 RCL 

053 01 01

054 33 x^2

055 54 )

056 55 ÷

057 53 (

058 02 2

059 65 ×

060 43 RCL

061 02 02

062 65 ×

063 43 RCL

064 03 03

065 54 )

066 95 =

067 02 INV

068 39 cos  (arccos)

069 42 STO 

070 04 04

071 92 INV SBR

Examples

Calculating a:

Set the TI-58/TI-59 to Degrees mode:

Input:

50° [ A ]

45  [ B ]  (b)

35 [ C ] (c)

[ D ] returns a:  35.00312885

85° [ A ]

100  [ B ]  (b)

70 [ C ] (c)

[ D ] returns a:  116.9607609

Calculating θ:

52 [ A ]  (a)

38 [ B ] (b)

49 [ C ] (c)

[ E ] returns θ:  72.15813198

80 [ A ]  (a)

60 [ B ] (b)

65 [ C ] (c)

[ E ] returns θ:  79.47338145

Note:  The next post will be on July 23, 2022.

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

TI-58/TI-59 Week: Hyperbolic Functions

 TI-58/TI-59 Week:  Hyperbolic Functions

Introduction

The program listing sets up the soft keys as the following:

[ A ] :  calculate sinh

sinh x = (e^x - 1/e^x) / 2

[ 2nd ] ( A' ):  calculate arcsinh (principal branch)

arcsinh x = ln | x + √(x^2 + 1) |

[ B ]:  calculate cosh

cosh x = (e^x + 1/e^x) / 2

[ 2nd ] ( B' ): calculate arccosh (principal branch)

arccosh x = ln | x + √(x^2 - 1) |

[ C ]:  calculate tanh

tanh x = sinh x / cosh x = (e^x - e^(-x)) / (e^x + e^(-x))

[ 2nd ] ( C' ):  calculate arctanh

arctanh x = ln | √((x^2 + 1) / (1 - x)) |

R00 is used in calculation.  Note:  INV ln x, e^x

Program Listing

000 76 LBL   (sinh x)

001 11 A

002 53 (

003 22 INV

004 23 ln x  

005 42 STO

006 00 00

007 75 -

008 43 RCL

009 00 00

010 35 1/x

011 54 )

012 55 ÷

013 02 2

014 95 = 

015 92 INV SBR  (RTN)

016 76 LBL   (arcsinh x)

017 16 A'

018 42 STO

019 00 00

020 85 +

021 53 (

022 43 RCL

023 00 00

024 33 x^2

025 85 -

026 01 1

027 54 )

028 34 √

029 95 =

030 50 |x|

031 23 ln x

032 92 INV SBR

033 76 LBL (cosh x)

034 12 B

035 53 (

036 22 INV

037 23 ln x 

038 42 STO

039 39 00

040 85 +

041 43 RCL

042 00 00

043 35 1/x

044 54 )

045 55 ÷

046 02 2

047 95 =

048 92 INV SBR

049 76 LBL (arccosh x)

050 17 B'

051 42 STO

052 00 00

053 85 +

054 53 (

055 43 RCL

056 00 00

057 33 x^2

058 75 -

059 01 1

060 54 )

061 34 √

062 95 =

063 50 |x|

064 23 ln x

065 92 INV SBR

066 76 LBL (tanh x)

067 13 C

068 53 (

069 22 INV

070 23 ln x

071 42 STO

072 00 00

073 75 -

074 43 RCL

075 00 00

076 35 1/x

077 54 )

078 55 ÷

079 53 (

080 43 RCL

081 00 00

082 85 +

083 43 RCL

084 00 00

085 35 1/x

086 54 )

087 95 =

088 92 INV SBR

089 76 LBL (arctahn x)

090 18 C'

091 53 (

092 42 STO

093 00 00

094 85 +

095 01 1

096 54 )

097 55 ÷

098 53 (

099 01 1

100 75 -

101 43 RCL

102 00 00

103 54 )

104 95 =

105 34 √

106 50 |x|

107 23 ln x

108 92 INV SBR

Examples

sinh 3.96;  3.96 [ A ] returns 26.21913142

arcsinh 40;  40 [ 2nd ] (A') returns 4.382182848

cosh -2.22;  -2.22 [ B ] returns 4.657969987

arccosh 100:  100 [ 2nd ] (B') returns 5.298292366

tanh 0.58:  0.58 [ C ] returns 0.5226654297

arctanh 0.96:  0.96 [ 2nd ] (C') returns 1.94591014906

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

TI-58/TI-59 Week: Adding Machine

TI-58/TI-59 Week:  Adding Machine

Introduction

Turn your TI-58 and TI-59 into an adding machine, which uses register R00 as the accumulator. 

The soft keys do the following functions:

[ A ]:  Clear the accumulator

[ B ]:  Add [ + ]

[ +/- ] B:  Subtract [ - ]

[ C ]:  Multiply [ × ]

[ 1/x  ] [ C ]:  Divide [ ÷ ]

[ D ]:  Add % 

[ E ]:  Recall the accumulator

Program Listing

000 76 LBL

001 11 A

002 00 0

003 42 STO

004 00 00

005 92 INV SBR (RTN)

006 76 LBL

007 12 B

008 44 SUM

009 00 00

010 61 GTO

011 15 E

012 76 LBL

013 13 C

014 49 Prd

015 00 00

016 61 GTO

017 15 E

018 76 LBL

019 14 D

020 55 ÷

021 01 1

022 00 0

023 00 0

024 65 ×

025 43 RCL

026 00 00

027 95 =

028 44 SUM

029 00 00

030 61 GTO

031 15 E

032 76 LBL

033 15 E

034 43 RCL

035 00 00

036 92 INV SBR (RTN)

Example

Clear the Register:  [ A ]

Add 15:  15 [ B ]   (Result:  15)

Add 30:  30 [ B ]   (Result:  45)

Triple:  3 [ C ]   (Result:  135)

20% Discount:  20 [ +/- ] [ D ]  (Result:  108)

Halve:  2 [ 1/x ] [ C ] (Result:  54)

Subtract 30:  30 [ +/- ] [ B ]  (Result:  24)

Add 50%:  50 [ D ]  (Result: 36)

Recall the register:  [ E ]  (Result:  36)

Enjoy the accumulator.  

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

TI-58/TI-59 Week: Numerical Derivative

TI-58/TI-59 Week:  Numerical Derivative

Introduction

The program estimates the numeric derivative:

d/dx f(x) = (f(x + h) - f(x)) / h

Registers used:

R01:  x

R02:  h

R03:  d/dx

Labels:

[ A ]:  store x

[ B ]:  store h

[ C ]:  calculate derivative

LBL E:  store f(x), assume x is in the display.  You can use registers R00 and R06 and above for registers.  Use Rad  ( [ 2nd ] [ - ] ) if f(x) contains trigonometric functions.  End each function with the steps =, INV SBR (RTN)

Function Listings

(step number, key code, key)

000 76 LBL

001 11 A

002 42 STO

003 01 01

004 92 INV SBR (RTN)

005 76 LBL

006 12 B

007 42 STO

008 02 02

009 92 INV SBR (RTN)

010 76 LBL

011 13 C

012 43 RCL

013 01 01

014 85 +

016 43 RCL

017 02 02

018 71 SBR

019 15 E

020 42 STO

021 03 03

022 43 RCL

023 01 01

024 71 SBR

025 15 E

026 94 +/-

027 85 +

028 43 RCL

029 03 03

030 95 =

031 55 ÷

032 43 RCL

033 02 02

034 95 =

035 42 STO

036 03 03

037 92 INV SBR (RTN)

038 76 LBL

039 15 E

...      .... ....

n-1 95 =

nnn 92 INV SBR (RTN)

Examples

f(x) = sin x;    Rad, sin

x = 0.5, h = 0.1, [ C ] returns 0.8521693479

x = 0.5, h = 1E-8, [ C ] returns 0.87755

f(x) = (1 + cos x)^1.5;   Rad, cos, +, 1, =, y^x, 1.5

x = 2, h = 0.01, [ C ] returns -1.035743295

x = 2, h = 1E-8, [ C ] returns -1.04206

f(x) = x * e^(x);   STO, 00, e^x * RCL, 00

x = 3, h = 0.01, [ C ] returns 80.84630054

x = 3, h = 1E-5, [ C ] returns 80.342648

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

TI-58/TI-59 Week: ML 13 Curve Solution

 TI-58/TI-59 Week:  ML 13 Curve Solution

Introduction

Today's blog entry highlights just one of the wonderful programs offered by Texas Instrument's Master Library.  

When the Master Library ROM program module is in the TI-58, TI-58C (for this week I will say the TI-58 to refer to both the TI-58 and TI-58C), and the TI-59, call up the Curve Solution by pressing [ 2nd ] [ LRN ] (Pgm) 13.  

The user keys are assigned as:

A:  enter the central angle in radians ( θ )

B:  enter the circle's radius ( r )

C:  enter the arc length ( s )

D:  enter the chord length ( c )

E:  solve for the sector area ( A' )

A':  solve for the central angle ( θ' )

B':  solve for the radius ( r' )

C':  solve for arc length ( s' )

D':  solve for the chord length ( c' )

E':  solve for segment area ( a' )

Enter two of the variables θ, r, s, and c and solve for the rest, and at least one of the two variables θ or r must be entered.  

Examples

Example 1:  Known: r and c

r = 10.8

c = 12.0

[ 2nd ] (Pgm) 13

10.8 [ B ]  ( r )

12.0 [ D ]  ( c )

[ 2nd ] (A'):  1.17806194 rad  ( θ )

[ 2nd ] (C'):  12.72306896  (arc length)

[ E ]:  68.70457237 (sector area)

[ 2nd ] (E'):  14.824706 (segment area)

Example 2:  Known: θ and s

[ 2nd ] (Pgm) 13 

30° angle:   30 [ ÷ ] 180 [ × ] [ 2nd ]  ( π ) [ = ] [ A ]   ( θ )

40 [ C ]  ( s )

[ 2nd ] ( B' ):  76.39437268 ( r )

[ 2nd ] ( D' ): 39.54463718 ( c )

[ E ]:  1527.887454 (sector area)

[ 2nd ] (E'):  68.86240923 (segment area)

A little detour from our usually programming the calculator ourselves, but it is sometimes more effective and efficient to take advantage of either advanced built in or mainstream modules.  Alas, we do return to programming next time,

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Calculus: Scaled Integration

Calculus:  Scaled Integration

Introduction

The take the integral:

∫( f(x) dx, A, B) 

The integral can be transformed to new limits C and D via linear transformation:

∫( f(x) dx, A, B) → ∫( g(y) dy, C, D)

Where the interval [ C, D ] has the smaller range than [ A, B ].

Set the transformation to:

y = m*x + β

C = m*A + β

D = m*B + β

Solving for m, β:

(C - D) = (A - B) * m

m = (C - D) / (A - B)

and

β = C - A * m = D - B * m

Solving y = m*x + β for x:

x = 1/m * (y - β)

Taking the derivative of both sides:

dx = 1/m  dy

The transformed integral:

∫( f(x) dx, A, B) → 1/m * ∫( f(1/m * (y - β)) dy, C, D)

Examples

Example 1:  

∫(x^2 - 5 dx, 10 ,16) but scale the integration interval to [1, 2].

A = 10, B = 16, C = 1, D = 2

m = (1 - 2)/(10 - 16) = 1/6,  1/m = 6

β = 1 - 10 * 1/6 = -2/3

x = 6 * (y + 2/3) = 6 * y + 4

Transformed Integral:

6 * ∫( (6*y + 4)^2 - 5 dy, 1, 2) = 1008

Example 2:

∫( e^x * ln(x + 2) dx, 0, 5) but scale the integration to [0, 1].

A = 0, B = 5, C = 0, D = 1

m = -1/-5 = 1/5,  1/m = 5

β = 0 - 0 * 1/5 = 0

x = 5 * y

Transformed Integral:

5 * ∫( e^(5 * y) * ln(5 * y + 2) dy, 0, 1) ≈ 262.8586594

Numerical integrals were calculated with the TI-36X Pro.  

When trying the Simpson's rule or Trapezoid rule, I find the smaller range does not really give better estimates.  But I am presenting the technique and if this helps in the future, great.  

Coming up:

July 11 - July 15, 2022:  TI-58 and TI-59 Week

Next Regular Blog:  July 23, 2022

Eddie  

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Numworks: Version 19.2 Is Available

Numworks:  Version 19.2 Is Available

19.2 Is Here

The full upgrade to software 19.2 is for Numworks N0110 and N0120 models.  Only some of the features will be available for the oldest version N0100. 

How do I know which version I have?  

1.  Press the Yellow Home button.

2.  Go down to Settings and press [ EXE ]

3.  Go down to the last option in the menu, About, and press [ → ]. 

4.  You will see the Software Version.  The last five characters of the FCC ID will tell you what model of Numworks you have.

To update your calculator, just open a browser like Google Chrome, plug in your calculator, go to the numworks.com website.  

Features

Some of the features of 19.2 are (from the Numworks page):

*  The Statistics App now offers four plots: Histogram, Boxplot, Cumulative Frequencies, Normal Probability Plot

*  Median-Median and Exponential regressions are added.

*  Lists are now available everywhere, including the main Calculation app.   List elements are accessed by using the parenthesis (example:  list(1)).  Unlike Python, the first element is designated as element 1.

*  Plots in the Grapher app can be set to any one of seven colors of the user's choosing.

*  Significant tests now include a graphical result in the Inference App

*  The memory for the Python app is increased from 32,000 to 42,000 bytes

*  In the Application menu, each of the apps are assigned to a shortcut key as follows:

1:  Calculation

2:  Grapher

3:  Solver

4:  Statistics (one variable stats)

5:  Regression (two variable stats)

6:  Inference

7:  Sequences

8:  Python

9:  Settings

More information here:  https://www.numworks.com/calculator/update/version-19/

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Retro Review: Casio BF-80

Retro Review:   Casio BF-80

A folding calculator with easy-to-calculate finance prompts.  

Quick Facts

Model:  BF-80  (Easy Banker Financial)

Company:  Casio

Years:  1985 (production run is probably the late 1980s)

Type:  Finance

Batteries: 1 x CR-2016

Operating Modes:  Chain

Number of Registers: 2 User registers:  M,  Kin/Kout 

Display:  2 lines

Features

The BF-80 is a dual-leaf calculator.  On the left side, you have a regular four-function calculator, including memory functions, percent, and the square root function.

On the right side is where all the financial functions the BF-80 are located:

[ Kin ]/[ Kout ]:  The BF-80's other user memory register.  Unlike register M, there is no register arithmetic.

[ HMS ]/[ <HMS ]:  Convert decimal to/from hours-minutes-seconds.  Use the [ HMS ] key to enter parts of time.  

Example:  Add 3.5 hours to 11:30:00

11 [ HMS ] 30 [ HMS ] [ + ] 3.5 [ = ] 

Result:  15°0°0 (15:00:00)

[ DATE ]:  The date key leads two of my favorite functions of all time:  days between dates and calculating a future date.   The format is yy - mm - dd  (no dashes for 21st century dates).  Years are entered as four digits, from 1901 to 2099.  

For most, if not all, calculators, the cash flow convention is not used.  

INST-FV:  Calculates the future value of an annuity.  Interest rate is entered as periodical rate. Note that deposits are made at the beginning of each period (annuity due).  The INST indicator turns on. 

Example:  I pay $500 a month in an account that pays 5% interest for 10 years.

[ INST FV ]   (INST indicator is on)

PMT?  500 [ ENTER ]

i%?  5 [ ÷ ] 12 [ = ] [ ENTER ] 

n?  10 [ ÷ ]  12 [ = ] [ ENTER ]

FV= 77964.641

Pressing [ INT ] gives the interest earned:  17964.641.

CMPD-FV:  Calculates the future value of a lump sum (present value).  The CMPD indicator turns on, and INT gives the accumulated interest.

CMPD-PV:  Calculates the present value of a future lump sum (future value).  The CMPD indicator turns on, and INT gives the accumulated interest.  

Both CMPD calculations use this equation:

FV = PV * (1 + i%)^n

LOAN-PMT:  Calculates the monthly payment of a loan due at the end of each month.  The loan is to paid without a balloon payment.  The LOAN indicator turns on.

PV?:  amount to be financed

i%?:  annual interest rate

m?:  number of monthly payments

Example:  What is the monthly payment of $8,293.00 loan with 6% interest over 6 years?

[ LOAN PMT ] (LOAN indicator is on)

PV? 8293 [ ENTER ]

i%?  6 [ ENTER ] (no dividing by 12 in LOAN mode)

m? 6 [ × ] 12 [ = ] [ ENTER ] (still enter the number of months)

PMT = 137.43896

Pressing [ INT ] gives the accumulated interest paid on the loan:  -1602.6051

LOAN-BNS:  Calculates the bonus payment of a separate (side) loan given the number of bonus payments and it's cycle.

k = number of bonus payments

d = number of months to the first bonus payment

PV = bonus loan amount

i% = annual interest rate of the bonus loan

Example:  What is the payment of a bonus loan of $4,412.00 with 3% interest.  The firs bonus cycle is every 3 months from the loan date, with 15 bonus payments.

[ LOAN BNS ]  (LOAN indicator is on)

PV?  4412 [ ENTER ]

i%?  3 [ ENTER ]  (annual rate, like LOAN-PMT)

k?  15 [ ENTER ] (number of bonus payments)

d?  3 [ ENTER ] (number of months prior to the first bonus payment)

BNS = 328.21123

Pressing [ INT ] gives the accumulated interest:  -511.16857

I guess that this is for loans where payments are due every few months instead of every month.  

The Percent Key

The percent key on the BF-80 works like most Casio calculators with a percent key.   

To add a percent:  n [ × ] p [ % ] [ + ]

To subtract a percent:  n [ × ] p [ % ] [ - ]

To find a percent ratio:  part [ ÷ ] whole [ % ]

Percent change:  new [ - ] old [ % ]

A Neat Calculator - An 1980s Version of a Smartphone App 

For it's time, the BF-80 offers calculator with quick, prompting calculations for the on-the-go business and finance student or profession.  Today, in the 2020s, the calculator of this time definitely would  be a smartphone app.  

Surprisingly buying a BF-80 was incredibly reasonable.   

Coming up:

July 11 - July 15, 2022:  TI-58 and TI-59 Week

Next Regular Blog:  July 10, 2022, then  July 23, 2022

Eddie

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.