The MU Key on a Four Function Calculator and Programs for the DM42/HP 42S

 The MU Key on a Four Function Calculator and Programs for the DM42/HP 42S

Not too long ago, I purchased this very colorful, four function calculator from the University I work at, the Dexin BST DX-818.

The DX-818 is powered by a solar panel with an option to be run by an AAA battery when using the calculator in less than bright light conditions. The AAA battery is optional.

A Standard Calculator

This calculator is the standard four function key calculator, complete with the square root function, percent function, the standard three memory keys (M+, M-, and MRC), and a grand total (GT) key. A grand total is started when calculations are completed by pressing the equals key [ = ]. The grand total is both recalled and cleared when the [ GT ] is pressed.

The Markup Equation

Before we head to the calculators, the mark up is a calculation of between selling price (new), cost (old), and mark up. The markup is ratio between the selling price and cost over cost and as expressed as a percentage (%):

MU = (selling price – cost) ÷ cost = (selling price ÷ cost - 1)

Solving for the other variables yield:

selling price = cost * (1 + MU)

cost = selling price ÷ (1 + MU)

In these equations, MU is expressed as a decimal.

If let the selling price be the new value and cost be the old value, then we have the equation for percent change (Δ%):

Δ% = (new – old) ÷ old = (new ÷ old - 1)

Similarly:

new = old * (1 + Δ%)

old = new ÷ (1 + Δ%)

In these equations, Δ% is expressed as a decimal.

The Markup Key (MU)

On this particular calculator, there is an [ MU ] key. This is the markup key. Apparently, there are two types of [ MU ] key, one set of syntax for Casio calculators with the [ MU ] key. An example of a Casio calculator with an [ MU ] key is the MJ-120D plus. They way Casio calculators use the [ MU ] key is a calculation:

cost [ MU ] markup percentage [ % ] returns selling price.

Immediately pressing [ = ] returns selling price – cost.

However, some calculators, like the colorful calculator featured (I really wish I knew the model number) with the [ MU ] have another syntax, and that is what I will address from here on out.

On this particular calculator, the syntax, using one of the four arithmetic functions is:

y < +, -, ×, or ÷ > x [ MU ]

No use of the equals key is needed, unless you want to add the result to the grand total.

The four calculations with the [ MU ] key, on this particular calculator (and possibly the NewYes calculators from China) are:

Key Sequence	Formula Used	Notes
Y [ + ] X [ MU ]	100 * (Y ÷ X + 1)
Y [ - ] X [ MU ]	100 * (Y ÷ X - 1)	Calculates markup or percent change (Δ%). Y = selling price, new value X = cost, old value
Y [ × ] X [ MU ]	Y * (1 + X ÷ 100)	Adds X% to Y. Calculates the new value (selling price) given old value (cost) (Y) and markup (X).
Y [ ÷ ] X [ MU ]	Y ÷ (1 – X ÷ 100)	Finds the original retail price given selling price (Y) and discount rate (X). This can also be used for gross-up calculations.

Sample Calculations

Problem	Keystrokes	Result
Determine 100 * (Y ÷ X + 1) with Y = 420, X = 25	420 [ + ] 25 [ MU ]	1780
An item that cost the company $14.75 sells for $19.99. Find the markup.	19.99 [ - ] 14.75 [ MU ]	35.5254237288 (≈35.53%)
A company manufactures a product with a unit cost of $32.84 and wants a 20% markup. What is the selling price?	32.84 [ × ] 20 [ MU ]	39.408 (about $39.41)
A product is currently on sale for $39.99. If the discount is 35%, what is the original retail price.	39.99 [ ÷ ] 35 [ MU ]	61.523076923 (about $61.52)

RPN Programming with the Swiss Micros DM42

Here are four RPN programs, which are were programmed using a Swiss Micros DM42, which can be used on the HP 42S (and probably the HP 41C).

Program MU+: Y [ + ] X [ MU ]

00 {17-Byte Prgm}

01 LBL “MU+”
02 ÷

03 1

04 +

05 100

06 ×

07 RTN

08 END

Program MU-: Y [ - ] X [ MU ]

00 {17-Byte Prgm}

01 LBL “MU-”
02 ÷

03 1

04 -

05 100

06 ×

07 RTN

08 END

Program MUMLT: Y [ × ] X [ MU ]

00 {12-Byte Prgm}

01 LBL “MUMLT”
02 %

03 +

04 RTN

05 END

Program MUDIV: Y [ ÷ ] X [ MU ]

00 {21-Byte Prgm}

01 LBL “MUDIV”
02 ENTER

03 100

04 ÷

05 1

06 X<>Y

07 -

08 ÷

09 RTN

10 END

Sources

 Casio. “MJ-120D Plus” https://www.casio.com/intl/basic-calculators/product.MJ-120DPLUS/ Accessed May 23, 2026.

Eaton, Glenn. “The Calculator MU Key” Eaton Family Website. Posted on June 30, 2017. https://eatonfamily.au/calculator-mu-key/ Accessed May 23, 2026.

“How to use the MU button on a calculator? #1” YouTube Short: @newyes1162. Posted December 5, 2022. https://www.youtube.com/shorts/OiS8yFKKJSU Accessed May 23, 2026

Eddie

All original content copyright, © 2011-2026. 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.

fx-3900PV Programs: Finance Factors

fx-3900PV Programs: Finance Factors

I’m revisiting the fx-3900Pv, which seems to be a hit. The last set of programs from May 3 of this year: https://edspi31415.blogspot.com/2025/05/casio-fx-3900pv-linear-system-poisson.html

Remember: When using the ENT (enter/input) command, we must enter a valid number and then the next step. The number that precedes ENT is not counted as a step and is not recorded.

Example: x + 9

In LRN (learn) mode (Mode EXP):

ENT (enter any number)

+

9

=

Casio fx-3900Pv: Simple Interest

maturity amount = principal amount * (1 + 0.01 * I%) * N ÷ 360

interest accrued = maturity amount – principal amount

I% = annual interest rate

N = number of days

The Act/360 method is used.

Code (23 steps):

ENT # enter principal amount (PV)

Kin 1

×

(

1

+

.

0

1

×

ENT # enter interest rate

×

ENT # enter number of days

÷

3

6

0

)

=

HLT # pause, display maturity amount

-

Kout 1

= # display interest accrued, end program

Example 1:

Inputs:

Principal Amount: 1,000.00

Rate: 5%

Number of Days: 30

Output (rounded to 2 decimal places)

Maturity Amount: 1,004.17

Interest Accrued: 4.17

Example 2:

Inputs:

Principal Amount: 360.00

Rate: 8%

Number of Days: 90

Output (rounded to 2 decimal places)

Maturity Amount: 367.20

Interest Accrued: 7.20

Casio fx-3900Pv: Compound Interest Factor with Compounding Periods

The following program calculates the compound interest factor:

factor = (1 + I% ÷ PYR) ^ (YRS × PVR)

where

I% = annual interest rate

PYR = payments per year (compounding periods)

YRS = number of years (N)

The factor is used in simple compound interest problems:

FV = PV × factor

where:

FV = future value

PV = present value

Code (19 steps):

(

1

+

.

0

1

×

ENT # enter interest rate

÷

ENT # enter payments per year

Kin 1

)

x^y

(

ENT # enter number of years

×

Kout 1

)

=

Example:

Find the compound interest interest factor for: I% = 5%, 12 payments a year, 4 years

Factor: 1.220895351

If an investor expects a $5,000.00 payoff, what should the investor pay?

PV = FV ÷ X

Keys: (with the answer from program displayed: [ 1/x ] [ × ] 5000 [ = ])

PV (rounded): 4,0953.36

Casio fx-3900Pv: Loan Annuity Factor

The following program calculates the loan annuity factor:

factor = ( ( 1 - ( 1 + I% ÷ PYR ) ^ (-YRS × PYR) ) ÷ ( I% ÷ PYR )

where

I% = annual interest rate

PYR = payments per year (compounding periods)

YRS = number of years (N)

The factor is used in loan problems without balloon payments, and assume that the payments occur at the end of each period (ordinary annuity):

PV = PMT × factor

where:

PV = present value

PMT = periodical payments

Code (30 steps):

ENT # enter interest rate

÷

ENT # enter payments per year

Kin 2

×

.

0

1

=

Kin 1 # K1 = I% ÷ PYR

ENT # enter number of years

×

Kout 2

=

Kin 2 # K2 = YRS × PYR = N

(

1

-

(

1

+

Kout 1

)

x^y

Kout 2

+/-

)

÷

Kout 1

=

Example:

A student buys a car at $35,619 (after taxes and fees). The student gets a six year loan at 5.7% and pays at the end of each month. What is the payment?

PMT = PV ÷ factor

where PV = 35619, I% = 5.7, PYR = 12 (monthly payments), YRS = 6

Running the program with inputs 5.7, 12, 6: 60.85819003

Payment: [ 1/x ] [ × ] 35619 [ = ]: 585.28 (rounded)

Casio fx-3900Pv: Sinking Fund Factor (Savings Account)

The following program calculates the sinking factor (used for savings accounts):

factor = ( (1 + I% ÷ PYR) ^ (YRS × PYR) – 1 ) ÷ (I% ÷ PYR)

The factor is used in determining the future value of savings plans with regular deposits made at the end of each period:

FV = PMT × factor

Code (29 steps):

ENT # enter interest rate

÷

ENT # enter payments per year

Kin 2

×

.

0

1

=

Kin 1 # K1 = I% ÷ PYR

ENT # enter the number years

×

Kout 2

=

Kin 2 # K2 = YRS × PYR

(

(

1

+

Kout 1

)

x^y

Kout 2

-

1

)

÷

Kout 1

=

Example:

A child’s parents opens up an account on the child’s first birthday. The parents contribute $200.00 per month for the next 18 years. The account pays a fixed rate of 3% per month. What is the value of the fund when the child turns 18?

Note: The account is opened on the child’s first birthday, hence 17 years pass.

FV = PMT × factor

where PMT = 100, I% = 3, PYR = 12, YRS = 17

Running the program with inputs 3, 12, 17: 265.69267

Future Value: [ × ] 200 [ = ]: 53,138.54 (rounded)

Until next time, stay safe and sane,

Eddie

All original content copyright, © 2011-2025. 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.

The content on this blog is 100% generated by humans. The author does not use AI engines and never will.

Spotlight: Calculated Industries QR Calc

Spotlight: Calculated Industries QR Calc <Title>

Quick Facts

Model: 3375

Name: QR Calc

Company: Calculated Industries

Timeline: 1993

Type: Quality Control, Statistics

Operating System: Algebraic

Digits: 7

Memory: 1 general purpose memory register plus specific variable registers 

Power: 1 CR-2032 battery

When I purchased the QR Calc, there was no manual with it. Normally, it wouldn’t present any issues because I can often find manuals online. That is not the case with the QR Calc. If there is any manual online, please email me. I’ll have to be more careful next time.

I apologize that I will not be able to describe all the functions but hopefully I describe enough features to give the reader a general idea. Please check out the sources below.

Features

Let’s start with the mathematical functions included: powers and roots (y^x, x². √), natural logarithm (ln), exponential function (e^x), reciprocal (1/x), arithmetic (+, -, ×, ÷), and the standard percent key which operates they people expect it to (%). The order of operations is enforced. Like a lot of calculators, the change sign (+/-) key is a shifted function.

The operating range of the calculator is 7 digits: -9,999,999 to 9,999,999. Any calculator that has a result outside of this range causes the QR calculator to display an error message.

The store key for the QR Calc is labeled [ Set ].

The function →PPM changes any number into n parts per million.

Example: 0.0014 →PPM displays 1,400 PPM.

Here are some functions I was able to find out and figure out:

Normal Distribution

The normal distribution functions calculate areas of the standard normal distribution, assuming that μ = 0 and σ = 1.

n [ nZ ]: lower tail probability (from -∞ to x = n)

n [ 2^nd ] (ModZ): probability from x = 0 to x = n

One Variable Statistics

The QR handles a single set of statistics with the following key and key sequences:

[ Add ]: Add a data point (Σ+)

[ 2^nd ] [ Add ] (Subtract): Subtract a data point (Σ-)

[ 2^nd ] [ + ] (S←→P): Toggle between standard deviation and population deviation (σn indicator)

[ x-bar ]: Calculate the arithmetic mean.

[ R ]: Calculate the range of the data.

[ 2^nd ] [ x-bar ] (N): Calculate the number of data points.

[ 2^nd ] [ R ] (σ): Calculate the deviation, depending on the deviation mode set.

[ Low ]: Returns the minimum value of the data set entered.

[ 2^nd ] [ Low ] (High): Returns the maximum value of the date set entered.

[ Skew ]: Skew. I’m not sure what formula the QR Calc uses because I have not been able to match results with any formula I found yet.

[ 2^nd ] [ Skew ] (Kurt): Excess Kurtosis. Kurtosis measures how concentrated the data is with respect to the mean.

The formula used for Excess Kurtosis:

μ4 = 1/n * Σ((xi – mean)^4)

kurtosis = μ4/s^4 – 3

Process Capability Indices

If a process is mature, that is a process that is regular and has been executed for a period of time, we can measure the capability index.

There are two capability indices:

Cp: for a centered analysis

Cpk: for a non-centered analysis. This metric is used for potential future performance.

Generally, we want these indices to be at least 1. Capable processes have an Cp index of 1.33 or higher.

Key strokes:

Enter the mean: [ Set ] [ x-bar ]

Enter the deviation: [ Set ] [ 2^nd ] [ R ] ( σ )

Enter the lower specification limit (based on the normal distribution): [ Set ] [ LSL ]

Enter the upper specification limit: [ Set ] [ 2^nd ] [ LSL ] (USL)

Each variable entered will have an indicator.

Calculate Cp: [ 2^nd ] [ Cpk ] (Cp)

Calculate Cpk: [ Cpk ]

Example:

LSL = - 1, USL = 1, mean = 0.05, deviation = 0.27

[ 2^nd ] [ × ] (AC) to clear out the registers if needed

0.5 [ Set ] [ x-bar ] (x-bar indicator is on)

0.27 [ Set ] [ 2^nd ] [ R ] ( σ ) (σ indicator is on)

1 [ 2^nd ] [ - ] (+/-) [ Set ] [ LSL ] (L indicator is on)

1 [ Set ] [ 2^nd ] [ LSL ] (USL) (U indicator is on)

Results:

Cp: 1.234568

Cpk: 1.17284

That is a pretty good process.

Formulas Used:

Cp = (USL -LSL) / (6 * σ)

Cpx = min((x-bar – LSL) / (3 * σ), (USL – x-bar) / (3 * σ))

Control Charts

We get to the main feature of the QR Calc: Control Charts and Capability Limits. On the back of the calculator, the QR Calc has a list of handy formulas.

The heart of the QR Calc is the table of constants that are used in control charts and limit charts. Often the chart limits are built on many samples of n data points each, where x-bar is the average of the sample averages, and R is the average of the range samples. We can also build chart limits with one sample. The QR Calc can only handle sample sizes from 3 to 25 data points.

Mean Control Chart Limits:

Lower: LCL-mean = x-bar – n * A2 * R

Upper: UCL-mean = x-bar + n * A2 * R

R Control Chart Limits:

Lower: LCL-R = n * D3 * R

Upper: UCL-R = n * D4 * R

A2, D3, and D4 are constants used in calculating control chart limits. Accessing these constants takes one argument, which is the sample size.

The A2 constant for a sample size of 3: 3 [ nA2 ] returns 1.023.

Below is a short table of constants, as determined by the QR Calc.

Sample Size n	Constant A2	Constant D3	Constant D4
5	0.577	0	2.114
10	0.308	0.223	1.777
15	0.223	0.347	1.653
20	0.18	0.415	1.585
25	0.153	0.459	1.541

Standard deviation can be estimated by using the average range ( R ) and another constant d2:

σ ≈ R / d2

Sample Size n	Constant d2
5	2.326
10	3.078
15	3.472
20	3.735
25	3.931

A table of constants from n = 2 to 25 can be found here:

https://sixsigmastudyguide.com/x-bar-r-control-charts/

Example:

Construct mean and range charts from a sample (n = 5):

3.995

4.26

4.37

4.44

4.58

Keystrokes:

(after clearing data)

3.995 [ Add ] 4.26 [ Add ] 4.37 [ Add ] 4.44 [ Add ] 4.58 [ Add ]

X-bar chart:

LCL: [ x-bar ] - 5 [ nA2 ] [ × ] [ R ] [ = ] Result: 3.991455

UCL: [ x-bar ] + 5 [ nA2 ] [ × ] [ R ] [ = ] Result: 4.666545

R chart:

LCL: 5 [ 2^nd ] [ nD4 ] (nD3) [ × ] [ R ] [ = ] Result: 0

UCL: 5 [ nD4 ] [ × ] [ R ] [ = ] Result: 12.36669

The QC calc has contains the E2 constant.

Final Thoughts

The functions that I still do not know about or have figured out are: TRGa, TRGb, RS a, RS b, %Low, and %High.

This review is incomplete. I will keep searching for a manual, I may have to buy another QR Calc.

This calculator is a rarity, and one worth checking out.

Sources

Hessing, Ted. “Process Capability (Cp & Cpk)” 6σSTUDYGUIDE.COM (no specific date give, first comment on November 19, 2014) https://sixsigmastudyguide.com/process-capability-cp-cpk/. Accessed January 2025.

Hessing, Ted. “X Bar R Control Charts” 6σSTUDYGUIDE.COM (no specific date give, first comment on April 17, 2018) https://sixsigmastudyguide.com/x-bar-r-control-charts/. Accessed January 2025.

Hewlett Packard. HP-65 Stat Pac 2 Cupertino, CA. https://literature.hpcalc.org/items/975 1975

Next time, I’m going to see if a manual comes with it. Not everything has a manual online.

Eddie

All original content copyright, © 2011-2025. 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.