Monday, April 29, 2019

Four Function and Desktop Calculators: The [ TAX+ ] and [ TAX- ] Keys

Four Function and Desktop Calculators: The [ TAX+ ] and [ TAX- ] Keys

A good subject for a Monday (start off the work week for most of us, me included)

The TAX+ and TAX- keys up close and personal  (Casio SL-300VC)


What is needed:  a calculator with [ TAX+ ] and [ TAX- ]

Introduction

On a four function or desktop calculator with the [ TAX+ ] and [ TAX- ] keys, you can perform tax calculations and financial calculations.  The primary key purpose of these keys is for sales tax.  The procedure for these calculations are (almost) universal.  However, the procedure to set such tax varies by manufacturer.

Casio:  Hold [AC] until the display blanks and refreshes.  Enter the tax rate and press [ % ] (RATE SET). 

Texas Instruments (TI-1795SV):   Enter the tax rate, press [ rate ], [ tax+ ] (store)

Canon:  Press [AC], [ TAX+ ] (SET), enter the rate, and press [ TAX+ ]

Sharp: Press [ CE/C ], [ CE/C ] (twice), [ TAX+ ], enter the rate, press [ TAX+ ]

Printing Calculators (various):  Set tax setting switch to SET, enter the rate, set the tax setting switch back to calculator mode.  Check your manual because printing calculators may vary.

My focus will be on four function and desktop calculators.  Procedures for printing calculators will probably vary.

Note:  I did the procedures listed in today's blog entry on both the Casio SL-300VC and Casio LS-123K.  For using independent memory, check to see if you have either a combined memory recall/clear key [MRC] (or [RM/CM on the LS-123K) or two separate keys ([MR] for recall and [MC] for clear).  For illustration purposes I will use [MRC]  (once for recall, twice for clear).   Remember that you can press [AC] to clear memory. 

Left:  Canon LS-123K (Green), Right:  Casio SL-300VC (Blue)


Note:  Pressing [AC] or [MRC] [MRC] will only clear the memory register, not the tax rate.

Contents

1.  Testing What Tax Rate is Stored in Memory
2. Price After Sales Tax and the Amount of Tax
3. Adding Taxable and Non-taxable Amounts
4. Calculating Use Tax
5.  Find the Taxable Amount Given the Grand Total (Total Plus Tax)
6.  Finance: Using [ TAX+ ] to calculate Future Value
7.  Finance: Using [ TAX- ] to calculate Present Value

For all the examples today, I have the tax rate set to 9.5%.  Please see the Introduction section above on how to set the tax rate.

1.  Testing What Tax Rate is Stored in Memory

This procedure is for any calculator that does not have a recall tax feature, although it works for these calculators too.

Procedure:

100 [ TAX+ ] [ - ] 100 [ = ]

Example:  (remember I'm using the tax rate set at 9.5% for all examples on this blog entry)

100 [ TAX+ ] [ - ] 100 [ = ]
Result:  9.5

2. Price After Sales Tax and the Amount of Tax

The [ TAX+ ] key performs two operations:

Press [ TAX+ ] once to calculate the total plus tax
Press [ TAX+ ] again to calculate the tax amount

Example:

An invoice shows of a purchase of equipment totaling $250.00.  Find the total after tax and the sales tax.

250 [ TAX+ ]
Display:  273.75   (total invoice:  $273.75)

[ TAX+ ]
Display:  23.75   (sales tax:  $23.75)


3. Adding Taxable and Non-taxable Amounts

Sometimes an invoice has both taxable amount and non-taxable amounts (such as most services, installation fee, sometimes freight, some food).  We can calculate the total invoice accurately with both the TAX and memory keys.  Start by clearing out the memory. 

Procedure:

[MRC] [MRC] taxable amount [ TAX+ ] [ M+ ] n
non-taxable amount [ M+ ] 
[MRC]  (recall memory)

Example:

Suppose has the invoice has:

A scanner that subject to sales tax:  $69.99
Computer services not subject to sales tax: $34.95
Sales Tax Rate:  9.5%

[ MRC ] [ MRC ] 69.99 [ TAX+ ] [ M+ ] 34.95 [ M+ ] [MRC]

The total invoice is $111.59   (8-Digit display shows 111.58905)


4. Calculating Use Tax

In certain states, such as California, use tax on a purchase can occur.  Where you take delivery determines what sales tax rate you would pay.  If a vendor does not charge the required tax, the use tax kicks in, which constitutes the remaining amount required from the buyer.  How to pay the use tax is beyond the scope of this blog entry. 

Procedure:

taxable amount [ TAX+ ] [ TAX+ ] [ - ] sales tax charged [ = ]

Example:

A purchase of a printer from an online store has a retail price of $164.79.  Sales tax of 8% was charged on the printer in the amount of $13.18.  The purchaser lives in a tax district that has a sales tax rate of 9.5%.  What is the use tax?

164.79 [ TAX+ ] [ TAX+ ] [ - ] 13.18 [ = ]  

The use tax is $2.48  (8-Digit display shows 2.47505)


5.  Find the Taxable Amount Given the Grand Total (Total Plus Tax) 

Sometime you know only the grand total of the invoice, but you need to find what was the taxable amount and the tax applied to that amount.  That is what the key [ TAX- ] is for.

Press [ TAX- ] once to calculate the taxable amount
Press [ TAX- ] again to calculate the tax amount

This is the inverse of the [ TAX+ ] key.

Example:

During an audit, we find an invoice from an electronics retail store for a purchase of a video projector.  However, only the total invoice is readable, in the amount of $187.44.  What is the retail price and what was the sales tax charged?

187.44 [ TAX- ]
Display:  171.17809   (taxable amount:  $171.18)

[ TAX- ]
Display:  16.261917 (sales tax:  $16.26)


6.  Finance: Using [ TAX+ ] to calculate Future Value

Time for a little unorthodox use of the TAX keys to calculate simple compound interest problems.  If you have an investment and you want to know how much your account will be in n periods (usually year), you can use the [ TAX+ ] [ = ] combination.

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

FV = future value
PV = present value
r% = interest rate, stored as the TAX rate
n = number of periods

Procedure:

[ MRC ] [ MRC ] 
present value [ M- ]
Loop:  [ TAX+ ] [ = ]   (do this n times for n periods)
(display future value)
[ M+ ] [ MRC ] 
(display interest earned)

Example:

You deposit $1,000.00 in a moderate to aggressive investment account that pays an average of 9.5% per year.  What is the balance after 5 years?  How much interest is earned in those five years?

[ MRC] [ MRC ] 
1000 [ M- ]
[ TAX+ ] [ = ]
[ TAX+ ] [ = ]
[ TAX+ ] [ = ]
[ TAX+ ] [ = ]
[ TAX+ ] [ = ]    (loop the last two keys 5 times)
Future value:  $1,574.24  (8-Digit display: 1574.2385)

[ M+ ] [ MRC ]
Interest earned:  $574.24  (8-Digit display:  574.2385)


7.  Finance: Using [ TAX- ] to calculate Present Value

Similarly, we can use the [ TAX- ] [ = ] combination to calculate the present value of a discounted note. 

PV = FV / (1 + r%)^n

FV = future value
PV = present value
r% = interest rate, stored as the TAX rate
n = number of periods

Procedure:

[ MRC ] [ MRC ] 
future value [ M+ ]
Loop:  [ TAX- ] [ = ]   (do this n times for n periods)
(display future value)
[ M- ] [ MRC ] 
(display interest earned)

Example:

You want to save $10,000.00 in five years.  You find an account that pays 9.5% annual interest.  How much will you need to deposit today to get that $10,000.00 goal in five years?

[ MRC] [ MRC ] 
10000 [ M+ ]
[ TAX- ] [ = ]
[ TAX- ] [ = ]
[ TAX- ] [ = ]
[ TAX- ] [ = ]
[ TAX- ] [ = ]    (loop the last two keys 5 times)
Present value:  $6,352.28  (8-Digit display: 6352.2775)

[ M- ] [ MRC ]
Interest earned:  $3,647.72  (8-Digit display:  3647.723)

What the [ TAX+ ] and [ TAX- ] Keys Calculate

With the tax rate r set:

[ TAX+ ] calculates:   number in the display * ( 1 + r/100)

[ TAX- ] calculates:  number in the display / (1 + r/100 )

Happy calculating and may all your calculations, and work weeks, be successful,

Eddie


All original content copyright, © 2011-2019.  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.

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