Wednesday, April 27, 2011

TI-36X Pro Review

TI-36X Pro Review

This is a review of the TI-36X Pro Calculator by Texas Instruments.


Originally, this was the TI-30X Pro that was sold in Europe during the Autumn of 2010. Unfortunately, the 30X Pro had many bugs and as a result Texas Instruments quickly pulled the calculator off the market.

Click on this link for an article on the TI30X_Pro . The website, which has this article, is maintained and run by Joerg Woerner, is an excellent site for Texas Instruments calculators, past and present.

Recently, Texas Instruments released the TI-36X Pro, based on the TI-30X Pro; thankfully without the bugs. I got this calculator on 4/25/2011 at an Office Depot store in West Covina, California (greater Los Angeles area).

What the 36X Pro Does

The TI-36X Pro is Texas Instruments answer to Casio's fx-115 ES and Sharp's EL-W516 calculators. The calculator is dual powered - solar for operation and battery for memory retention. The 36X-Pro is designed to allow user to enter expressions exactly the way they are normally written. Exponents have a superscript, fraction bars can contain expressions, and answers can be shown in fraction form, decimal form, and if applicable, radical form or coefficients of π.

The 36X-Pro welcomes a return of the definite integral, something that has been missing on TI non-graphing calculators since the TI-68 (we are talking the late 1980s). In addition, the 36X-Pro adds the numerical derivative, sums (Σ), and products (Π).

Although the 36X-Pro enjoys a TI-84+ interface, the calculator features buttons that cycle through a list of functions with repeated presses of a button. They are:

ln log button: ln, log, log to any base
e 10 button: e^ (exponential function), 10^
π e ι button: the constant pi, the constant e, √-1 (for working with complex numbers)
sin button: sin, sin^-1, sinh, sinh^-1
(cos and tan buttons work similarly)
! nPr nCr button: factorial (integers only), permutations, combinations

The variable button works the same way, cycling through eight variables (an ALPHA key would SO much better). Thankfully, all the calculus functions require that x be the dummy variable, requiring only one press of the variable button.

Sadly the percent function still doesn't "work". All it does is divide the number attached to the % by 100. Hence typing 21.99 + 9.75% returns 22.0875, not 24.134025 (what it should be).

The 36X-Pro is function rich: prime factorization, fraction and integer extraction, absolute value, polar to rectangular conversions and vice versa, modulus, basic matrix operations, basic vector operations, base n conversions, logic functions, and random numbers. For statistical regressions, you are not limited to linear. Quadratic, Cubic, Logarithmic, Power, and Exponential are available. A trend that I am also seeing in non-graphing scientific (and financial) calculators is that distribution calculations are offered. For the 36X-Pro, this includes the Normal distribution and inverse (from a lower tail area), and discrete distributions Poisson and Binomial.

The numeric solver on the 36X-Pro works pretty quickly for most equations. You do not have to set each equation equal to zero, the calculator allows you to enter the equation as is. You also get 2 and 3 systems of equations. A cool feature of the simultaneous solver is that if the calculator will let you know if the system has no solutions or infinite solutions For the 3x3 case, equations for which solutions cam be found. Example: x = -168/11 + 12z, y = 72/11 - 4z, z = z.

The polynomial solver works with quadratic and cubic equations.

The 36X-Pro has one OP function that you can store simple macros. The macro takes one number as input. You can store the final result (only the final result) into a variable. The OP is good for quick functions and one-step recurrence relations. It won't do multiple step functions, loops, or comparisons. Examples of macros include "*2+3" and "+x→x". There is also an expr-eval (evaluate expression) function that you can temporarily store an expression with variables, including calculus functions (x is the dummy variable). Be aware that the evaluation function works one time. There is also a table mode, but the expression is in terms of x, so the table feature is not good for sums (Σ), integrals, or derivatives.

As far as complex number calculations are concerned, you are limited to arithmetic, square, cube, reciprocal, absolute value, angle, real and imaginary part extraction. The nice thing is that you can evaluate more complex functions with complex numbers...if you know the formulas.

The 36X-Pro has 20 common conversions (English-Metric, Temperature, Speed, Length, Pressure, Power, Electricity) and 20 common physical constants in SI units. (meter-kilogram-second system)

What I Like

* This is the most advanced non-programmable Texas Instruments scientific calculator since the TI-68, and it's solar!
* The operation is integrated: you do not have to switch to a separate matrix mode, complex mode, vector mode etc, to take advantage of these functions. This is my one big gripe about the Casio fx-115ES.
* I like the multiple touch keys - they clean up the keyboard (see exception below)

What I am not crazy about

* Only one key to access eight variables. To get the variable a, you have to press the variable key FIVE times. Yikes! TI was better off making an Alpha key and assign an alphabetical variable (and possibly θ) to each key.
* The arithmetic keys are chrome on silver - if it were not for the etchings, I would not be able to see the arithmetic symbols.
* Limited complex number functions. However, it is common that complex number functions on a calculator are usually limited.

Worth the buy?

I say yes. The 36X-Pro is a nice calculator and well designed. I say it is comparable to the Casio fx-115ES and Sharp EL-W506 both in terms of speed and overall functionality. For the time being, the 36X-Pro is offered in select stores, but I suspect that within a few months this calculator will be everywhere competing with the fx-115ES for shelf space in stores everywhere. I paid $21.99 for it.

Calculator Forensics: 9.000001562

What's in the Package

* TI-36X Pro Calculator with hard case and quick reference card
* A detailed and sturdy pocket manual. You can download the manual online from TI's website.

Happy Calculating!

Texas Instrument's TI-36X_Pro_Page

Wednesday, April 20, 2011

HP 10bii+ Review

This is the review of the Hewlett Packard HP 10bii+ financial calculator.

The HP 10bii+ is a substantial upgrade to the HP 10bii. Hewlett Packard finally utilized the keyboard to its fullest, adding many functions such as depreciation, probability distribution calculations, bonds, expanded statistic capabilities, and depreciation just to name a few.

For this review, I have worked out all the examples prescribed in the manual provided. I also worked some of the examples with other finance calculators (10bii, 12c, 17bii+, 30b) just to see if the calculators have consistent answers. I am happy to report that the 10bii+ is consistent with the other financial calculators.

As for speed, I would state from the testing I did so far, the speed of the 10bii+ is pretty much on par with the 12c (two-battery edition) and the 30b.

The Keyboard

The colors on the keyboard are nicer and brighter than its predecessors. I can actually see the blue shifted functions in all levels of light and angles. The keys are tactile and easy to push. No missed keystrokes during normal operation.

Thankfully, the HP 10bii+ it can take a spill and clean up easily, and no, I did not plan that. I was able to clean the calculator immediately and it works in perfect order.


The 10bii+ sports 20 memory registers: 0 through 9 and .0 through .9. Store arithmetic is provided, but not recall arithmetic. There is a dedicated M register with three keys dedicated to it: →M (store to M), RM, and M+. I really like this feature, which allows me to calculate a sum of a large amount of numbers. The M register has been a feature on the 10b series since the beginning.

The memory allocation for cash flows and data points are as follows:
* Up to 45 cash flows can be stored.
* Up to 45 data points can be stored - if you want the full statistical features of the 10bii+.

There is a catch though. The 10bii+ allows space dedicated for 15 cash flows and 15 data points. There are 30 slots that are shared between cash flows and data points. Once the slots are filled, and you will no longer be able to store cash flows. However, the manual states that you can continue to add data points at a cost: you can no longer review data points and the only have linear regression available. More on cash flows and statistics later.

One nit picky point, the STO function is still a shifted function (orange). Personally, I like STO to be a primary function (unshifted), but no big deal.

You can also recall mostly anything by first pressing RCL then the variable or storage register you want.


With the new 10bii+, you gain a ton of new mathematics functions:
* The constant π = 3.141592653589793...
* Trigonometric functions: sine, cosine, tangent and their inverses. Just remember if you want inverses, activate INV first (blue shift, M+ key)
* Hyperbolic functions and their inverses
* Permutations and Combinations
* The factorial function now serves ALL real numbers from -252.999999999 (nine 9s) to 253.119. I like this a lot, became the gamma function is one my favorite functions. Γ(x) = (x - 1)!
* Random Numbers from 0 to 1.
* Radian and Degree modes, but not angle conversions.

Calculator Forensics asin(acos(atan(tan(cos(sin(9))))))

Degree Mode: 8.99999864267

Chain or Algebraic

The 10bii+ offers to operating modes: Chain or Algebraic. Chain mode is obvious: any operations act immediately on the displayed number. Order of operations are ignored. The Algebraic mode is not of the "enter the entire expression and then press enter" type. For one argument functions, enter the number first then press the function.


2 ln(12.5) + sin(30°) would require the key presses

2 x 12.5 [orange shift] [2 key for LN] + 30 [blue shift] [÷ key for SIN] =

(answer 5.55145728862)

I wish HP would have implement RPN (Reverse Polish Notation) mode - even if the mode just turned the left and right parenthesis into swap the x and y registers (x<>y) and roll the stack down one level (R↓), respectively.

Last Answer... and a Bug?

The 10bii+ offers a last answer feature, which is new to the 10b series. The last answer is what was in the display when the equals key (or any key that finishes an operation, I think) was last pressed. The last answer can be accessed by pressing RCL =.

But there is a bug. While working the example on page 41 of the manual:

Here is how it was presented in the manual:

50 INPUT (Display: 50)
22 + 14 [orange shift] [% key for %CHG] (Display: -28. last answer is supposed to have 36)
60 INPUT (Display: 60)
RCL = (Here the display is supposed to say 36, but I get 60 instead)
[orange shift] [% key for %CHG] (Display is supposed to say -40, instead I get 0)

My guess is that pressing INPUT also loads the displayed number in the last answer register.

Two Ways to Operate Two Argument Commands

The 10bii+ presents two ways to work with two argument commands: use of the INPUT, and the direct, "in-line" way.

The INPUT way is the classic way in the 10b series: number or operations, INPUT key, number or operations, function key(s).

The direct way is: number, function key(s), number, = key. Personally, I prefer this method - more straight forward.

You get the option with: combination, permutation, Student's t Distribution functions, percent change, DATE function, days between dates function.

Time Value of Money

The time value of money keys on the 10bii+ work (nearly) exactly like the time value of money keys work on any other HP calculator. The interest key (I/YR) works with annual interest rate (the 12c series work with the periodic interest rate). Solving time value of money problems are straight forward: enter the known amounts, press the variable to be solved for by just pressing the key. No compute key necessary.

For those of you new to HP financial calculators, Chapter 5: Picturing Financial Problems and Chapter 6: Time Value of Money on the full manual provide an excellent introduction and a good set of practice problems regarding time value of money.

New: a dedicated clear time value of money function. No more C ALL required - nice!

Profit Calculations

Calculations regarding cost, price, margin, and markup follow the model of the time value of money application. Enter the known information, then press the key of the desired variable to solve for it.

Cash Flows

At first glance, it looks like the cash flow application was untouched. Not so. This application is updated - BIG TIME.

First we get not one, but two ways of entering repeated cash flows:

The classic way:
Cash flow, CFj key, frequency, [orange shift], [CFj key for Nj]....

And the INPUT way, which I am a fan of:
Cash flow, INPUT key, frequency, CFj key

Next, like the time value of money registers, there is an all important clear cash flows sequence.

Third, when net present value (NPV) is calculated, you also calculate net future value (NFV). NFV is accessed by the SWAP function after NPV is calculated.

Finally, we can now review cash flows and their frequencies. This is done by simply pressing RCL CFj. Cash flows and frequencies can be reviewed, added, inserted, and deleted.

Date Calculations

One of my favorite calculator features have finally made it to the 10bii+: date functions! Dates can be entered in U.S. Format (mm.ddyyyy) and International Format (dd.mmyyyy). Two functions are available: Days between Dates and Date Addition. For example, if today is April 21, 2011 - then I am alive a grand total of 12,456 days. :)


If you are familiar with the bond functions on the 12c, them you should at home with the 10bii+. There are separate storage registers for Settlement Date, Maturity Date, Coupon Rate, and Call Amount. You can calculate the price of the bond, yield to maturity, and the accrued interest. With many dedicated keys to bonds, you can keep track of what each variable contains.


The breakeven application is similar to the time value of money application. Enter amounts for the known variables then solve for the ones you want.


Straight Line, Sum of the Years Digits, and Declining Balance are available. Too bad declining balance with crossover is not (for calculating depreciation for tax purposes). The depreciation functions use the time value of money variables:

N for number of periods
I/Y for declining rate (if applicable)
PV for cost
FV for salvage value

The depreciation functions calculate the year's depreciation, and the remaining book value. The functions only work in whole years - meaning you will not be able to set up the first month. If you want to work with non-integers (say the asset has 5 1/2 years), you can calculate the first five years, but the calculating the sixth year returns 0. A possible work around in this Case is to use the remaining book value from year 5 as the 6th (and final) year of depreciation.

Statistics and Distributions

The statistics application is similar to the cash flow application. You can review entries and edit them, there is a clear data points sequence, and you can easily find the most common statistics measurements (mean, deviation, sums).

I was surprised to find that the 10bii+ has six regressions:
1. Linear, y = m x + b
2. Logarithmic, y = m ln x + b
3. Exponential, y = b exp(m x)
4. Power, y = b x^m
5. Exponent, y = b m^x
6. Inverse, y = m/x + b

The variables m, b, and the correlation coefficient (r) can be found by pressing the orange shift, the appropriate key, the orange shift key again, and then swap. The 10bii+ also features best fit (Regression 0). However, to find which regression fit the data points better, you will have to attempt to either predict x or y, or calculate a weighted average. One thing that can be improved is that the 10bii+ actually stating the best fit when it is activated.

The 10bii+ also has lower tail normal distribution and Student's t distribution CDF function and their inverses. I think labeling the distribution functions LTND (lower tail normal distribution) and Student (lower tail student's distribution) may have been better than z <>p and df,t <> p , respectively. But it works, and works well.

What's Impressive

* A well written full manual, which is available on CD or online. Now if the writers finish the last example in Chapter 13...
* The ability to review and edit cash flows and data points.
* Distribution functions and the fact that the factorial function coves real numbers
* Date functions, bonds, and depreciation have been added
* Unlike the 30b, you don't have to dig through menus to find functions, everything for the most part is on the keyboard

Wish List

* RPN mode
* When best fit mode is activated, you are told what regression model is selected without having to calculate a prediction first
* A better case, something similar to the one used for the 17bii+
* A "K" indicator when the constant function is used

Manual Curiosities

This covers Edition 1

* Page 41: RCL = does not work (well) after pressing INPUT
* Page 119: the paragraph comparing standard deviation and population deviation is repeated four times on this page
* Page 154: net future value example is not complete


I would recommend purchasing the 10bii+. It is a very solid calculator good for the entry level while having a lot of easy to use finance applications. Hewlett Packard has stepped up their game by updating the 10b series.

Great work, Hewlett Packard!


Monday, April 18, 2011

HP 10bii+ First Look

Hi Everyone!

I am going to present a first look at the new Hewlett Packard HP 10bii+ financial calculator. This is a continuation of HP's 10b's series.

A Little History

Hewlett Packard first introduced us to the HP 10b series with the classic HP 10b in 1988. The original featured time value of money calculations, interest conversions, 14 cash flows, with each flow allowed to be repeated up to 99 times, linear regression, percent change, and profit solvers (cost-sell-margin-markup).

The original HP 10b had 15 storage registers, however 6 of them were for statistics.

In 2001, Hewlett Packard updated the HP 10b with the HP 10bii. The function set remained pretty much the same, except there were only 10 memory registers. The trade off was that all the statistics measurements had dedicated registers.

In 2011, Hewlett Packard introduced the next member of the 10b line, the HP 10bii+. Here is a picture of it:

The 10bii+ At A Glance

From the picture alone, I can tell that the Hewlett Packard really packed this calculator with features. In addition to the features that the 10b line already has, the 10bii+ adds:

* Bond Calculations
* Days Between Dates Calculations
* Breakeven Calculations
* Depreciation
* Trigonometry and Hyperbolics
* Random Numbers
* Distributions: Normal and Student's t
* Proper Algebraic Mode. Calculator can be made to follow the proper order of operations.

No RPN (Reverse Polish Notation), bummer, but not a deal breaker.

One of the first features I noticed on the 10bii+ was that the factorial function is now extended to the real numbers. This is what happens when I try to calculate 2.5! on the 10bii:

I get an error message. Now when I calculate 2.5! On the HP 10bii+:

I get 2.5! = 3.3234 (to four decimal places). This is already seems like this a serious upgrade to the HP 10bii+.

In my next post I will review the many new features of the HP 10bii+. At first glance the 10bii+ looks impressive. I wish that the case that comes with it was not so snug.

What's in the Package

* Calculator
* Case
* Quick Start Guide
* CD containing the full manual in many languages, and I mean many languages: English, Spanish, French, Arabian, Japanese, Portuguese, and Italian just to new a few.

Saturday, April 16, 2011

Hi everyone! This is my very first blog. My aim is to have a blog of math and calculators. I will add blogs whenever I get a chance.

Have a great day!

HP 15C: Pythagorean Triples

HP 15C:   Pythagorean Triples This program calculates the Pythagorean triple (A, B, C) such that A^2 + B^2 = C^2 by the formulas: ...