## Friday, March 30, 2018

### Retro Review: Texas Instruments TI-54

Retro Review:  Texas Instruments TI-54

General Information

Company:  Texas Instruments
Type:  Scientific
Memory:  7 memory registers
Battery:  2 x LR-44 or 2 x AR-76
Years:  1981 - 1983
Original Cost: \$40
Operating System: AOS, Immediate Execution
Storage Arithmetic:  +, -, *, ÷, ^, roots, percent change

It’s good to finally to get the calculator that accompanies the Scientific Calculator Sourcebook that I bought years ago.

Features

The TI-54 is a scientific calculator with a lot of additional features over the typical non-programming scientific calculator that was released at the time.

Percent Key (Δ%)

I think the percent works backwards than modern calculators.   Press the new value first, then [2nd] ( Δ% ), then old value, [ = ].

Example:  Percent change from 32 to 56:  56 [2nd]  (Δ%) 32 [ = ] 75  (75% increase)

Combinations and Permutations

Like the TI-55 III, the arguments for combination and permutation functions take one argument in the form of nnn.rrr.

Example:

Combination where n = 25, r = 5 is entered as 25.005 [2nd] [ 9 ] (nCr)
(Result: 53,130)

Permutation where n = 25, r = 5 is entered as 25.005 [2nd] [ 8 ] (nPr)
(Result:  6,375,600)

Rectangular/Polar Conversion

[2nd] [x<>y] (P-R):  to Rectangular.  Input:  r [x<>y] θ [2nd] [x<>y] (P-R).  Result: y [x<>y] x.

[INV] [2nd] [x<>y] (P-R):  to Polar.   Input x [x<>y] y [INV] [2nd] [x<>y] (P-R).  Result:  θ [x<>y] r.

Statistics

The TI-54 has one variable and two variable statistics, with linear regression of the equation y = a * x + b.   The b/a key gives the intercept and slope.  Predictive values and correlation are also available.

Extra Functions

The TI-54 also has percent change, absolute value, fractional part, and integer part.

Other Functions

Other functions include degree/degree-minutes-seconds conversions and constant operations with [ K ].

Complex Numbers

Perhaps the biggest attraction of the TI-54 is the complex number mode.  Complex mode is activated as soon as the complex number is entered.

To enter complex numbers:

Rectangular:  b [ Img ] a

Polar:  θ [ θ ] r

Since the display is one number, the real part/magnitude is default shown.  To show the complex part, press [ EXC ] [ Img ]/[ θ ] to show the imaginary part/angle.  The user will know if that the imaginary part/angle is shown by the CMPLX indicator is flashing.

The amount of functions to complex functions offered are greater than most scientific calculators would offer, which is impressive at the time:  arithmetic, power, natural logarithms, exponentials, square root, and square.

Keyboard

Scientific calculators that were produced from Texas Instruments in that era (early 1980s) had a reputation for their not so great keyboards, affecting TI-54, TI-55 II, and TI-57.  Unfortunately, the keyboard is the Achilles’ Heel for this model.  On occasion, pressing the key doesn’t register, and occasion the key registers twice.  This problem is prevalent on the number keys.   So operating the TI-54 will require patience and maybe a few extra presses of the [ON/C] key.  Other than this, the TI-54 worked well.

Verdict

If you are to purchase a TI-54, please be aware of possible keyboard issues, other than that it is a good calculator.

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions

### Scientific Calculators Two Ways of Entering Complex Numbers

Scientific Calculators Two Ways of Entering Complex Numbers

On scientific calculators, there are two primary ways complex numbers are entered:

1. Using the [ a ] and [ b ] keys

2. Using a + bi notation

Complex Numbers using the [ a ] and [ b ] Keys

Calculators:  Canon F-605, Sharp EL-501X, Texas Instruments TI-35 Plus, Texas Instruments TI-52, most bargain Dollar Store calculators

This applies to most basic level scientific calculators.  Only arithmetic operations and polar/rectangular conversions apply in this mode.

Entering complex numbers:   real part [ a ] imaginary part [ b ]

Entering polar complex numbers (for conversion to rectangular complex numbers only):  magnitude [ a ] argument/angle [ b ]

Please be aware that in this mode where the [ a ] and [ b ] keys have to be used, the order of operations are not followed.

Example:  (3 + 3i) + (2 + 3i) * (4 + 3i)
(What is really calculated:  ((3 + 3i) + (2 + 3i)) * (4 + 3i))

Key Strokes: (in complex mode)
3 [ a ] 3 [ b ] [ + ] 2 [ a ] 3 [ b ] [ × ] 4 [ a ] 3 [ b ] [ = ]

Result:  2 + 39i (2 is stored in a, 39 is stored in b)

Example:  Transform 8 – 3i to Polar representation, use degrees mode

Key Strokes: (in complex mode)
Press [ DRG ] until the calculator is in Degrees mode (DEG indicator)
8 [ a ] 3 [ +/- ] [ b ] [ 2nd/SHIFT/INV ] (RP, rθ)

Result:
([ a ]) 8.544003745  ( r )
[ b ] -20.55604522 ( θ )

Complex Numbers using the a + bi Notation

Calculators:  most multi-line scientific calculators (Casio fx-115ES, fx-991ES, fx-991 Classwiz, Texas Instruments TI-36X Pro, Sharp EL-W516, Canon F-792SGA, most graphing calculators

Complex numbers using a + bi notation are entered exactly as they are written.  This mode is present on more advanced scientific calculators, particular the multiline calculators, as well as all graphing calculators.   The ability to calculate and display complex numbers may be turned on in a separate mode, or turned on through a set up menu.

Typically the available functions for complex numbers are:

* Arithmetic
* Inverse
* Square
* Polar/Rectangular Conversion
* Absolute Value
* Argument
* Real and Imaginary Parts
* Conjugate
* Square Roots (graphing calculators, all HP calculators with complex numbers)
* Exponentials and Logarithms (graphing calculators, all HP calculators with complex numbers)
* Powers, both real and complex (graphing calculators, all HP calculators with complex numbers)
* Trigonometric functions (TI-85, TI-86, TI-89, Casio Classpad, all HP calculators with  complex numbers)

In this complex numbers mode, the order of operations is followed.

Example:  (3 + 3i) + (2 + 3i) * (4 + 3i)

Key Strokes:  (*key strokes may vary)
[ ( ] 3 [ + ] 3 [ i ] [ ) ] [ + ] [ ( ] 2 [ + ] 3 [ i ] [ ) ] [ × ] [ ( ] 4 [ + ] 3 [ i ] [ ) ]

Result:  2 + 21i (2 [ Re<>Im ] 21)

Example:  Transform 8 – 3i to Polar representation, use degrees mode

Key Strokes: (in complex mode)
Press [ DRG ] until the calculator is in Degrees mode (DEG indicator)

Alternative 1:  (8 – 3i) >rθ,  (8 – 3i)>Polar

Alternative 2:
r:  abs(8 – 3i)
θ: angle(8 – 3i), arg(8 – 3i)

Result:
8.54003745 -20.5604522,  8.54003745*e^(-20.5604522*i)

That is two primary ways how complex numbers are entered on scientific calculators.

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.

## Monday, March 26, 2018

### HP Prime: Length of a Loan with a Certain Payment

HP Prime:  Length of a Loan with a Certain Payment

Introduction

The program PMTLENGTH will calculate how many payments that are required to finish a loan, given a certain annual interest rate and payment.  Payments are assumed to be monthly, and end of period.  The program will also return the last payment.  Due to the rounding in the financial algorithms, the last payment is an approximate (unless the interest rate is 0%).

Input:  PMTLENGTH(I,P,X)
I = annual interest rate
P = loan amount
X = payment amount, enter as a negative amount

Firmware 13441 or later is required.

HP Prime Program PMTLENGTH

EXPORT PMTLENGTH(I,P,X)
BEGIN
// I%YR, PV, PMT (as negative)
// 2018-03-19 EWS
// how many monthly payments?
// last payment? (FV)

LOCAL N,B;

N:=Finance.TvmNbPmt(I,P,X,0,12);
B:=P;
IF FP(N)≠0 THEN
B:=Finance.TvmFV(IP(N),I,P,X,12);
N:=IP(N)+1;
END;

// {N, final pmt}
RETURN {N,B};
END;

Examples

Example 1:  How long will I take to pay off a \$2,000 loan if I make \$600 payments each month?  This is a no interest loan.

Result:  {4, -200}

It will take 4 payments, with the last payment being \$200.

Example 2:  How long will I take to pay off a \$5,350 loan if I make \$750 monthly payments each month?  The loan has a 10% monthly interest rate.

Result:  {8, -286.906502677}

It will take 8 payments, with the last payment being about \$286.91.

Eddie

This blog is property of Edward Shore, 2018.

## Saturday, March 24, 2018

### Favorite Solar Calculators – Six Years Later

Favorite Solar Calculators – Six Years Later

Favorite Solar Calculators – Reading that Blog Entry Today

On June 10, 2012, I listed some of my favorite solar calculators of all time:

I still love the TI-25X Solar, I wish the screens weren’t so damn fragile!  I went through two of them.

I have two fx-115 ES Plus calculators, one gray and one black.  The black looks much better!

Maybe one day I’ll get the BA 35 Solar again from eBay.  Maybe I will give the Casio FC-200V a second shot.

As of March 2018, Casio fx-3650pII is the current edition of the fx-3650P.  The fx-3650PII is in the shape of the fx-115ES/991ES/300ES/82ES Plus.  That’s about it from what I can get from research:  still four program areas with 360 steps and 7 variables.

No, Casio still currently sells the fx-3650PII only outside the United States, which means for us Americans, we have to order online.  An open invite to Casio to stock the office stores and university stores with this model in the States is extended.

The current Sharp EL-W516 edition, the EL-516WT, eliminated the formula storage, eliminated the catalog, and reduced the definable keys from 4 to 3, I am not happy about that.

Three More Inductees

I have three more to add to the list I posted in 2012:

Casio fx-991EX Classwiz – 2015 – Present

The Classwiz model is the next step in Casio solar powered calculators.  They have an icon menu, like their graphing calculators, and there is an [OPTN] key that allows users to specific mode-specific functions.  Modes includes computation (COMP), complex numbers (arithmetic, polar/rectangular conversions), base integers, matrices up to 4 x 4, vectors, statistics, distributions, basic spreadsheets up to 5 x 45, equation solving, inequalities and ratios.  The newest feature is the QR function that will take a screen shot of the calculator, or in some cases, statistical graphs, which can be retrieved from the Casio QR Website or app.

I can only hope the next iteration the Classwiz and the fx-3650P or fx-50FII merge so programming will be included.

TI-30 SLR+ – 1987 – 1990s

This is a bigger version of the TI-25X Solar (TI-30X Solar internationality).  This calculator completely runs on solar and light power.  What I look about this better than the TI-25X are the keys and the fact the display isn’t so fragile.  See my detailed blog of it here:  https://edspi31415.blogspot.com/2014/09/ti-30-slr-and-memories-of-school.html

Casio fx-260 Solar II (we can included the Casio fx-260 Solar, fx-82 Solar, fx- 82 Solar II)
Original fx-260 Solar/fx-82 Solar:  2000s – present
Current fx-260 Solar II/fx-82 Solar II: 2017 – present

I don’t know what I was thinking when I skipped this model last time.  The fx-260 offers a wide variety of functions:  trigonometry, logarithms, fractions, degrees and degrees-minute-second conversions, polar/rectangular conversions, and one variable statistics.  This is great calculator for those who want a small, compact, calculator that attacks the basics.  The fx-260 series is completely solar powered.  Pictured is the newer fx-260 Solar II, which the mode markers have been mode to the back of the calculator case.  Can’t beat the classics.

Eddie

This blog is property of Edward Shore, 2018.

## Monday, March 19, 2018

### Review: Canon F-605 Scientific Calculator

Review:  Canon F-605 Scientific Calculator

Company:  Canon
Type:  Scientific
Memory:  7 registers
Battery:  LR54 x 1
Years:  Current (4/172015-)
Cost: around \$10
Number of Functions: 154
Operating System:  Immediate Execution

On a trip to Fry’s for computer headphone/microphone set, I always head to the aisle where the calculators are.  Besides the “dollar store calculators” and printing calculators, every one Fry’s had I have their model.  Except for the F-605, which was packaged in a box.  So to the check stands I went, with the F-605, a \$2 A+ Homework scientific calculator, and headphone set in tow.

Another Clone of the Sharp EL-501X… or is it?

At first glance, the Canon F-605 looks like a clone of the Sharp EL-501X.  Sure, it has it’s complex numbers, complete with the [ a ] and [ b ] keys, the keyboard is nice and compact, and it has its base conversions with one variable statistics.  Close inspection, the F-605 differs from the EL-501X in a number of ways.

By the way, I reviewed the Sharp EL-501X in July 2014, which you can click here to see:  http://edspi31415.blogspot.com/2014/07/sharp-el-501x-today-vs-ti-35-plus-1989.html

Features

The display has 10 digits, but carries 14 internal digits.

We have our scientific functions, logarithmic functions, exponential functions, hyperbolic functions, decimal degrees/degrees-minutes-seconds conversions and power and root.  The [ F←→S ] converts the display from floating to scientific notation.

For the polar/rectangular conversions, the [ a ] and [ b ] keys are used.  [ a  ] is used for x and r, while [ b ] is used for y and θ.

Here is where the Canon F-605 starts separating itself from the rest of the clones.  The F-605 offers fractions, with fraction/decimal conversions and improper/proper fraction form conversions.

The F-605 has a random number function which generates numbers from 0 to 1, which has three digits.

One of the great surprises the F-605 has is that it has seven memory registers, A through F, and M.  There are also the arithmetic storage functions M+ and M-.  The nice thing is that all seven memory registers are available on all the modes, except for statistics, where M is not available.

Base Display Modes (except for Decimal) is limited to arithmetic. To convert numbers, just call their respective mode. There are still no Boolean functions, just arithmetic.

The Complex number mode only allows for complex number arithmetic.  The [ a ] and [ b ] are keys to enter and display the real and imaginary parts.  You still can use rectangular/polar conversions.  ( [ a ]:  real/abs, [ b ]: imaginary/argument)

The F-605 has one variable statistics.  In addition to mean, deviation, and sums, the F-605 offers the minimum and maximum of the data set.  In statistic mode, parenthesis and store to M keys are used for accessing statistical results.  You can’t use parenthesis in stats mode on the F-605.  One thing I am very happy about, unlike most of the scientific calculators in this family, the F-605 has it Statistics mode on a key other than ON/C!  Yes, putting a mode as the second function of the clear button is very annoying.

Keyboard

The keyboard is very clean, and fonts are readable.  The keys do have a rubbery feel, but so far, out of the using it, I have no complaints about the response.  The calculator is very light weight.

Verdict

If you are looking for an inexpensive \$10 (or possibly less) scientific calculator and you don’t want a solar calculator, I can recommend the F-605.  I would say that the F-605 is just above the Casio fx-260 Solar or Sharp EL-501X.

Eddie

This blog is property of Edward Shore, 2018

## Saturday, March 17, 2018

### HP Prime: Advanced Payments for a Lease

HP Prime:  Advanced Payments for a Lease

Introduction

The program ADVPMT calculates the monthly payment of lease several payments are paid simultaneously at the beginning of the lease.

Firmware 13441 is used.   This program uses the TmvPV function from the Finance App.  The “Finance.” suffix will allow the program to be used regardless of which app HP Prime is set to.

BEGIN
// 2018-03-15 EWS
// HP 17BII+
LOCAL X;
X:=(−P-S*
Finance.TvmPV(N,I,0,−1,12))/
(Finance.TvmPV(N-A,I,−1,0,12)+A);
RETURN ROUND(X,2);
END;

Example

Find the monthly payment of a 48 payment, 4.6% lease where 3 payments are required in advance.  The amount financed is \$10,000 with an expected salvage value of \$2,000.

Result:  -263.54

Each payment will be \$263.54, with the first payment being three times that amount, or \$790.62.

Source:
Hewlett Packard.  HP 17bII+ Financial Calculator User’s Guide  Edition 3, 2007  San Diego.

Eddie

This blog is property of Edward Shore, 2018.

## Wednesday, March 14, 2018

### Pi Day 2018

Happy Pi Day!  Here I am celebrating with a couple of 41s (Hewlett Packard HP 41C, Swiss Micros DM41L).

Happy Birthday Albert Einstein

RIP Stephen Hawking

π = 3.1415926535...

If you want to calculate many digits of pi, there are many ways to do this.  If you have a TI-89 or HP Prime, please check out this blog from November 2016: https://edspi31415.blogspot.com/2016/11/ti-89-and-hp-prime-approximation-digits.html

Happy Pi Day!

Eddie

This blog is property of Edward Shore, 2018

## Tuesday, March 13, 2018

### HP Prime: Car Payment and Affordability

HP Prime:  Car Payment and Affordability

Introduction

The two programs presented here tackle common financial questions of purchasing automobiles.  (or other equipment).   CARPMT calculates what would be the monthly payment, while CARAFFORD calculates the sticker price that the buyer can afford.  The variables that are considered are:

N = number of monthly payments, typically 48, 60, or 72 (for 4, 5, or 6 year term, respectively)
I = annual interest rate of the buyer can get, hopefully this rate is low
S = sales tax rate
D = discount rate, as car dealers tend to off discounts
W = down payment (enter as negative)

Firmware 13441 is used and the Finance app functions TvmPMT and TvmPV are used.  For the finance functions, they are designated with the “Finance.” prefix to allow usage of the program on any app.   TVM cash flow convention is retained, outflows (payments) are entered as negative while inflows (in this case the financing loan) are treated as positive.

HP Prime Program CARPMT

EXPORT CARPMT(N,I,P,S,D,W)
BEGIN
// enter down pmt as negative
// 2018-03-12 EWS
// Function Setup
// no. payments,
// annual interest, price,
// sales tax, discount, down pmt

LOCAL X;
X:=P*(1+S/100)*(1-D/100)+W;
// Finance app
X:=
Finance.TvmPMT(N,I,X,0,12);

RETURN ROUND(X,2);

END;

Example:
Term:  60 months
Interest Rate: 4.5%
Sticker Price: 18995
Sales Tax: 9.5%
Discount Rate: 10%
Down Payment: \$1000

CARPMT(60,4.5,18995,9.5,10,-1000)

Result:  -330.35

Payment is \$330.35

HP Prime Program CARAFFORD

EXPORT CARAFFORD(N,I,X,S,D,W)
BEGIN
// pmt and down pmt enter
// as negative
// 2018-03-12 EWS
// Function Setup
// no pmts, annual interest,
// payment (as pqsitive),
// sales tax, discount, down pmt

LOCAL P;
// Finance app
P:=
Finance.TvmPV(N,I,X,0,12);
// calculating affordable price
P:=(P-W)/((1+S/100)*(1-D/100));

RETURN ROUND(P,2);

END;

Example:
Term:  60 months
Interest Rate: 4.8%
Payment:  \$350.00
Sales Tax: 9.5%
Discount Rate: 10%
Down Payment: \$500

CARAFFORD(60,4.8,-350,9.5,10,-500)

Result:  \$19,418.67
The car that can be afforded is \$19,418.67 (before sales tax and discounts).

As day of this post is on Pi-Day Eve, Happy Pi Day on March 14!  π = 3.141592653…

Eddie

This blog is property of Edward Shore

## Sunday, March 11, 2018

### Fun with the Texas Instruments TI-60

Fun with the Texas Instruments TI-60

Notes:

1.  I like to have the user input all the values into the registers before running the program.  This way, we can save program steps because the calculator doesn’t have to stop to ask for inputs.  Also, you don’t have to change all the values for different problems.  Finally, R/S can be used for only output.

2.  I keep register 0 (R0) out so that the user can have at least one register to store immediate results in further calculations.  I list the minimum partition for each program.

Great Circle Distance (in miles)

Formula:
D = acos (sin ϕ1 * sin ϕ2 + cos ϕ1 * cos ϕ2 * cos (λ1 – λ2)) * 3959 * π/180

Note: for kilometers, replace 3959 with 6371.

Where:
ϕ1, ϕ2:  Latitude of locations 1, 2; north is positive, south is negative
λ1, λ2:  Longitude of locations 1, 2:  east is positive, west is negative

Store before running:
R1:  ϕ1 as a decimal (convert from DMS if necessary)
R2:  λ1
R3: ϕ2
R4: λ2
Set the TI-60 in degrees mode.

Program (41 steps) – 2nd Part 5:
 PG OP Key PG OP Key 00 71 RCL 21 04 4 01 01 1 22 54 ) 02 32 SIN 23 33 COS 03 65 * 24 95 = 04 71 RCL 25 12 INV 05 03 3 26 33 [COS]  (COS^-1) 06 32 SIN 27 65 * 07 85 + 28 03 3 08 71 RCL 29 09 9 09 01 1 30 05 5 10 33 COS 31 09 9 11 65 * 32 65 * 12 71 RCL 33 91 π 13 03 3 34 55 ÷ 14 33 COS 35 01 1 15 65 * 36 08 8 16 53 ( 37 00 0 17 71 RCL 38 95 = 18 02 2 39 13 R/S 19 75 - 40 22 RST 20 71 RCL

Example:

Los Angeles:  ϕ = 34°13’ = 34.21666667°, λ = -(118°15’) = -(118.25°)
London:  ϕ = 51°30’26” = 51.50722222°, λ = -(0°7’39”) = -(0.1275°)

Result:  5431.617778 mi

Tip: For DMS-DD conversions: if you have a negative angle, enter the angle without the negative sign, do the conversion DMS-DD, then press [ +/- ].

Impedance of a Series Resonance Circuit

This program gives both the magnitude and phase angle.

Impedance:   Z = R + j*(ω*L – 1/(ω*C))
Where:  ω = 2*π*F
Magnitude:  abs(Z)
Phase Angle:  arg(Z)

Variables:
R = resistance ( Ω )
C = capacitor ( farads )
L = inductor ( henrys )
F = Frequency (Hz)

Store before running:
R1:  R
R2:  C
R3:  L
R4:  F
Set the TI-60 in degrees mode.

Program (35 steps) – 2nd Part 5:
 PG OP Key PG OP Key 00 02 2 18 02 2 01 65 * 19 54 ) 02 91 π 20 76 1/x 03 65 * 21 95 = 04 71 RCL 22 61 STO 05 04 4 23 05 5 06 95 = 24 71 RCL 07 61 STO 25 01 1 08 05 5 26 52 X<>Y 09 65 * 27 71 RCL 10 71 RCL 28 05 5 11 03 3 29 12 INV 12 75 - 30 38 [P-R] (R-P) 13 53 ( 31 13 R/S 14 71 RCL 32 52 X<>Y 15 05 5 33 13 R/S 16 65 * 34 22 RST 17 71 RCL

Example:

Input:
R1:  R = 11.56 Ω
R2:  C = 0.0002 F
R3:  L =  0.018 H
R4:  F = 72 Hz

Results:
Phase Angle (θ) = -14.12679136°
Magnitude = 11.92049981

Linear Interpolation

Given points (x0, y0) and (x1, y1) with x0 < x < x1, we can estimate y by linear interpolation by:

y = ((x1 – x)*y0 + (x – x0)*y1)/(x1 – x0)

How good of an approximation depends on how close x0 and x1 are, and whether the curve that is being approximated is close to linear.

Store before running:
R1:  x1
R2:  y1
R3:  x2
R4:  y2
R5:  x

Program (34 steps) – 2nd Part 5:
 PG OP Key PG OP Key 00 53 ( 17 01 1 01 53 ( 18 54 ) 02 71 RCL 19 65 * 03 03 3 20 71 RCL 04 75 - 21 04 4 05 71 RCL 22 54 ) 06 05 5 23 55 ÷ 07 54 ) 24 53 ( 08 65 * 25 71 RCL 09 71 RCL 26 03 3 10 02 2 27 75 - 11 85 + 28 71 RCL 12 53 ( 29 01 1 13 71 RCL 30 54 ) 14 05 5 31 95 = 15 75 - 32 13 R/S 16 71 RCL 33 22 RST

Example:

Input:
R1:  x1 = 2
R2:  y1 = 3
R3:  x2 = 4
R4:  y2 = 8
R5:  x = 3

Result:
y = 5.5

Purchase of a Car:  How much can I afford?

The program will calculate the sticker price (price before sales tax) of an automobile that you can afford.  You give the term you want, the interest rate you qualify for, the sales tax rate, and the maximum payment you can afford.  This assumes that you don’t put any money down.

Formulas:
A = P/I * (1 – (1 + I)^-N) / (1 + S)

A = sticker price of the car
P = monthly payment
I = monthly interest rate of the loan, in decimal.   I = rate/1200
N = number of months.  N = years*12
S = sales tax rate, in decimal.  S = sales tax rate/100

Input:
R1:  number of payments
R2:  monthly interest rate
R3:  payment
R4:  sales tax rate, in decimal

Program (30 steps), 2nd Part 4:
 PG OP Key PG OP Key 00 71 RCL 15 45 y^x 01 03 3 16 71 RCL 02 55 ÷ 17 01 1 03 71 RCL 18 94 +/- 04 02 2 19 54 ) 05 65 * 20 55 ÷ 06 53 ( 21 53 ( 07 01 1 22 01 1 08 75 - 23 85 + 09 53 ( 24 71 RCL 10 01 1 25 04 4 11 85 + 26 54 ) 12 71 RCL 27 95 = 13 02 2 28 13 R/S 14 54 ) 29 22 RST

Example:

Input:
R1:  number of payments = 60, (5 year term)
R2:  monthly interest rate = 0.05/12 = 0.004166667, (5% annual interest rate)
R3:  payment = 400
R4:  sales tax rate, in decimal = 0.095, (9.5%)

Result:  19357.34

In this example, the highest sticker price that can be afforded is \$19,357.34 (before sales tax).

I enjoy programming with the TI-60, unlike most Texas Instruments calculators that have keystroke programming, the TI-60 shows the step and key code you have entered instead of advancing to the next step with code 00.

Eddie

This blog is property of Edward Shore, 2018.

### TI-84 Plus and Casio fx-CG50: Which Die Wins?

TI-84 Plus and Casio fx-CG50: Which Die Wins? Introduction:  Which Die Wins?   The program DICEODDS compares a pair of dice against eac...