financial calculators

8/8/2019 Financial Calculators

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Preface to the Book

The application manual for the financial calculator (FC200V) is being prepared with a view tohelp in understanding the functional part of the calculator. In the process help from varioussources containing the mathematical and statistical formula have been taken, utmost care hasbeen taken not to copy the data from these sources.

The examples wherever necessary has been provided to understand the operational part ofthe calculator.

The area of mathematics is very vast and understanding completely by one person is verydifficult. The sample book is designed to help all users to have the conceptual knowledgecoupled with practical aspect of the same.

Happy computing!


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APPLICATION MANUALFINANCIAL CALCULATORS FC100V, FC200V

Specific Applications in addition to various other applications that can be performed by FC are

summarized below:

Simple Interest Calculation

Compound Interest calculation

Cash Flow Calculation

Amortization calculations

General and function calculation

Statistics calculations

Interest rate conversion calculations

Cost / selling price / margin calculations

Day or date calculation

Depreciation calculation

Bond (Annual/yield to maturity (YTM) calculations)

Break even point analysis


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Explanation

Example

Operation

Simple Interest calculation

Simple Interest calculations as performed mainly by banks and loan providers or personlending or borrowing funds at simple rate of interest. The formula for calculation shall be asfollows:

SI = PV x n / 365 x I% PV= PrincipalN = Number of interest periods

SFV= PV+SI I = Annual interest rateSI = Simple InterestSFV=Interest + principal

Principal (PV) = INR 5000 5000x90/365x9/100Interest (I %) = 9%Days (n) = 90SI = solve =110.95SFV = solve =5110.95

Press key and using the cursor key enter the following data with exe key

1

2

3

For calculating the simple interest bring the cursor key to SI and enter the solve key and the

answer appears as 1 above Press ESC key and bring the cursor by using the Key and enter theSolve key and the answer appears as 2 and using the ESC key bring the cursor to ALL key and

press SOLVE key and the answer appears as 3 above.

Note: The days in a year can be adjusted as 360 days or 365 days depending upon the usageto adjust press SMPL and then SET key and enter EXE key and chose the option of 360

or 365 days.

Simple Int.Set : 365 or 360 daysDys : 90I% : 9PV : 5000SI : Solve

SFV : SolveALL : Solve

SI= -110.958904

SFV= -5110.958904

SI= -110.958904SFV=-5110.958904

An amount of 5000/- is borrowed at the rate of 9% per annum for 90 days, calculate thesimple interest.


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Explanation

Operation

Compound Interest calculation

Most of the banks and person dealing with funds use the word compounding interest annually,semi-annually or quarterly etc. to understand better compound interest would meancalculating the interest on interest also. The mathematical formula shall be as follow:

C.I. = P , where C.I. = compound interest

If the interest rates for the successive fixed periods are r1%, r2%, r3% ..., then A

(amount) is given by

A=P ... .., where A= amount & principal , P= principal

For example continue with the same example in previous sheet. If the period is 3 years thenCI would be

C.I. =5000 x {(1+ .09)-1} = 1475.145A =5000 + 1475.145 = 6475.145

Press CMPD key

Input the following using scroll and exe keys

* Use of option PMT is explained in next page

Note: Using scroll key please enter the P/Y = 1 and C/Y = 1 as the same represents the

Installments per year and Compounding per year respectively. If the compounding issemi annually then C/Y should be selected as 2 and for quarterly the same should be

selected as 4.

Note: Press ESC key to come back to previous screen

Note: To clear variables from the memory is to press SHIFT key and 9 key and EXEkey and chose the correct option to clear either setup, memory or allvariables from the memory

Set : begin / end select End using scroll and exe keyN : press 3 and enter exe keyI% : press 9 and enter exe keyPV : press 5000 and enter exe keyPMT : leave blank or press 0 and enter exe key*FV : Press solve key, see the answer appears as -6475.145


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EMI calculation CMPD continues.

A very important tool for finance companies having the business of lending money and all

those also borrowing money and in the need to know that how much monthly installment needto be paid for a particular loan.

Typically a person needs to know the present value of amount borrowed/lend and the interest

rate to be paid also the total number of installments to be used while returning the amountborrowed. i.e.

PV = amount borrowed or lend i.e. INR 50000

I% = interest rate i.e. 12% p.a. i= I%/12/100 = 0.010N = number of installments per year i.e. 15 years = 180 times

A typical way of calculating the EMI shall be taking the help of computer or a long sheet of

paper and lot of time in computing and yet not very sure about the way of doing. The formulashall be as follows:

PV x i x (1+ i)

=(1+ i)-1

= 50000 x 0.01 x (1.01)180

(1.01)180

- 1

= 600.08

EMI calculation without a calculator having the solving power like this is just impossible anddoing little simulations and variations in interest, principal etc, the working becomes verytough, but the use of FC 200V is very simple, faster and economical, lets see

Press CMPD key and using the scroll and exe key enter the following data

Set = End key

N = Press 180 and enter Exe key (15 years x 12 months)I% = Press 12 and enter Exe key

PV = 50000 exe keyPMT = Solve key

FV = Press 0 and enter Exe keyP/Y =12 as the installments per year is 12 the duration of loan is 15 years

C/Y =12 as the compounding also is monthly so in a year 12 compounding


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Scroll back to PMT key and enter solve key as the answer flashes -600.08.

Is it not quite amazing the result is produced in less than a minute as against probably one

hour?

Now we can use variation just like mortgage calculators available on the web and computerspreadsheets e.g.

1. Calculate the PV if we know how much maximum EMI can be paid

2. Calculate the maximum Rate of interest can be borne if EMI, period and PV is

known

3. Calculate the Number of periods (i.e years) wherein loan can be repaid if PV, I%and EMI is known

Just in simple way skip the term we want to know and enter the data in rest of the terms as

before, using the scroll key come back to the term we want to know and press solve key andresult is available.

Set = End keyN = 180 periods (15 years x 12 months)

I% = 12PV = solve key

PMT = -600.08FV =0

P/Y =12 as the installments per year is 12 the duration of loan is 15 yearsC/Y =12 as the compounding also is monthly so in a year 12 compounding

Set = End keyN = 180 periods (15 years x 12 months)I% = Solve keyPV = 50000PMT = -600.08FV =0P/Y =12 as the installments per year is 12 the duration of loan is 15 yearsC/Y =12 as the compounding also is monthly so in a year 12 compounding

Set = End keyN = Solve keyI% = 12PV = 50000PMT = -600.08FV =0P/Y =12 as the installments per year is 12 the duration of loan is 15 yearsC/Y =12 as the compounding also is monthly so in a year 12 compounding


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Explanation

Example

Cash Flow Calculation

The application mainly is used by analysis to appraise an investment proposal having a fixed

stream of cash inflow after a fixed period of cash outflow. Typically an investor need to knowthe following to do the analysis i.e. cash outflow and cash inflow and certain financial tools to

help him to take the decision, the tools could be Internal Rate of Return (IRR), Net PresentValue (NPV), Net Future Value (NFV) and Payback Period (PBP)

PBP The payback period is defined as the number of years required to recover a projects

cost.

NPV The net present value (NPV) method discounts all cash flows at the projects cost ofcapital and then sums those cash flows.

Accept project if NPV > 0.

IRR The internal rate of return (IRR) is defined as the discount rate which forces a

projects NPV to equal to zero.

Accept project if IRR > cost of capital.

A typical cash flow shall work out as follows

Cash Inflow

Cash Outflow

An investment would outlay an expenditure of INR 100000 in the year0 and thereafter for thenext four years it generates the cash inflow at a consistent flow of 40000 per year.

The PBP shall work out to be like 100000/40000=2.50 years


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The NPV shall be as follows:

Particulars cash In/Out Discounted Cash Flow @12%

Year 0 -100000 -100000 -100000.00

Year 1 40000 40000/ (1.12) 35714.28

Year 2 40000 40000/ (1.12) 31887.75

Year 3 40000 40000/ (1.12) 28471.21

Year 4 40000 40000/ (1.12) 25420.72

Net present value +21493.96As you know, money devalues over time. The rate at which it does is commonly referred to as

the "discount rate". Therefore, let's say you have a payment/income profile as shown aboveand we assume a discount rate of 12%. If you take the difference between the net present

value of the payments and the net present value of the returns, you get the net present valueof the investment. In the case shown above that turns out to be 121493.96-

100000=21493.96. (NPV)

IRR

If we equate the net present value to zero we get the internal rate of return, a rate which putscash outflow-discounted cash inflow equal to zero, the significance of IRR is that for example

the IRR for the above said case is 21.86% and if the money devalues at 22% then you makenothing on your investment. So prudence say that you must make investment that fetches

you return greater than 22%.

The IRR can be derived only be trial and error method and a guessed cost of capital should beestimated otherwise the trial and error method also takes long time and is irritating.

The common method used for IRR is

CF+ CF +CF +CF +CF = 0

(1+r) (1+r) (1+r) (1+r)

In the given case if we discount the cash flow by an estimated rate of capital of 21% shallgive us the NPV equal to +1617.64Again using the trial method we forward the rate to 22% and see the NPV coming out to beas -254.38 but the object is to bring the discounted cost of capital equal to Zero so by usingthe trial and error method we use the following

Formula

1617.6421% + ----------------- X 1

1617.64+254.38

= 21.86% (IRR)

We have seen how cumbersome procedure is used to calculate the IRR and NPV imagine aperson evaluating the 50-100 proposals a day shall get mad and crazy. The solution providedby FC 200 V is quite simple and we just have to input the data as follows:


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Operation

For calculating the NPV at the discounted rate of 12%

Press Cash Key and using the scroll and exe key input the data as follow

*remember to remove the I%=12% / 21.86% otherwise the PBP shall be calculated on

DCF@12% and the result shall be 3.15 years / 3.99 years

Is it not very simple and clean way of computing complex things, yes thanks to FC 200V

Remember to be patient while solving IRR as calculator processes the data at the speed of _

Note: Data editor can input the maximum number of 80 variables in case of 1-var is selected

or 40 in case of 2- var is selected (i.e. X, Y or X and Freq ) and 26 in case of X, Y andFreq is selected. To choose the option Press STAT Key and chose 1- Var press exe and

AC key and select again CASH key and in the case of more than one variable using thesame procedure above select other than 1-Var mode.

I% : input 12 enter exe keyCsh : Press exe key and input that cash out flow and cash inflow

Cash outflows should be represented as (-) and inflow as (+): using ESC key and scroll key press following

NPV : Press solve key and the result shall be +21493.97IRR : Press solve key and the result shall be 21.86%PBP : Press solve key and the result shall be 2.50 years*NFV : Press solve key and the result shall be +60000*


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Explanation

Example

Operation

Interest rate conversion calculations

The conversion of annual interest rate into effective interest rate is usually used when thecompounding per year is more than one. The conventional way of calculating EEF (effectiveinterest rate) is:

EEF = 1+APR/100

n- 1 x 100 APR Annual percentage rate (%)

n EEF Effective interest rate (%)N number of compounding

APR = 1+EEF/100 1/n

- 1 x n x 100

n

Example of converting the annual rate is where an investor gets the return on an investmentother than annual basis then his first curiosity shall be to know what my effective annualinterest rate is. E.g.

Interest rate: 12% compounded semi annually, the EEF shall be 12.36% and if the EEF is 14%then APR shall be 13.54%. Similarly if the compounding can be quarterly (4) or monthly (12)and accordingly results can be obtained but how complex is to solve the power of 12.

Press CNVR key

Input the above data using scroll and exe key

Other way could be press i% =14 and press APR key the result shall be 13.54% as describedabove.

N = Press 2 and enter Exe key

I% = Press 12 and enter exe key

EEF = press solve key and the result is 12.36%


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Explanation

Operation

Cost / selling price / margin calculations

Cost and their relation with the selling price is very well known, the difference is known asmargin which could be profit or loss. The formula for calculation shall be as follows:

CST = SEL * (1-MRG/100)CST= costSEL= selling priceMRG=margin

SEL = CST/ (1-MRG/100)

MRG = (1- (CST/SEL))*100

Select COST Key

By inputting any two values the third value can be calculated, by using the following way, itcan be done:

Note: By inputting any two variables thirdvariable can be calculated, typicallymargin is the selling price less cost

and divided by selling price as the%age of sale price, conversely many

people use the cost as the base price for generating the %age of value addition to thecost.

CST = Press 1200 and enter exe key

SEL = Press 1500 and enter exe key

MRG= press solve key answer shall be 20%


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Explanation

Example

Amortization calculations

Amortization means "the systemic payment plan -- such as a monthly payment -- so that your

loan is paid off over the specified loan period."

So an amortized loan is for one specific amount that is to be paid off by a certain date, usually

in equal monthly installments. Your car loan and home loan fit that definition. Your credit card

account doesn't because it's a revolving loan with no fixed payoff date.

A part of the payment goes toward the interest cost and the remainder of the payment goes

toward the principal amount -- the amount borrowed,"

Interest is computed on the current amount owed "and thus will become progressively smalleras the ending balance of the loan reduces."

In simple meaning when you borrow money the first repayment of loan installment, theinterest is on the full amount of loan but as you continue to pay back the principal amountkeeps on reducing so is the interest amount.

But if you want to know the breakup of any EMI or installment into Principal and Interest it

shall be a quite difficult task for common man.

Let us understand the concept of amortization in simple amortization calculator. The concept

of PMT, interest, FV, BAL, INT, PRN, INT, PRN ETC can be understood with an easy

example.

In the given case the PV = 10000 and interest rate is 2% and the PMT working out to be286.43 over a period of 3 years i.e. N=36 months, please note the Amortization table helpsyou to calculate the interest and principal on any of the installment specified. The requirement

is to know the PMT = EMI = -286.43 (remember EMI can be calculated by CMPD key),PV=principal = 10000 and Interest = i%=2. You can calculate between any month to any

month i.e. PM1 to PM2, remember that PM2 needs to be greater than PM1.

0

60

120

180

240

300

Amount

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Months

Break up of PMT

InterestPrincipal


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Operation

Finding the breakup of any PMT for any month shall be difficult task, however the same shallbe quite easy in FC200, see the steps

1. The answer pertains to the principal balance after 25th installment, please refer thetable

2. The answer pertains to the interest component in the first installment (PM1) pleaserefer the table

3. The answer pertains to the principal component in the first installment (PM1) pleaserefer the table

4. The answer pertains to the total interest paid from 1

st

to 25

th

installment please referthe table5. The answer pertains to the total principal paid from 1st to 25th installment please refer

the table

The simulation from any installment to any installment is possible, quite simple way.

Note : for going back to default input screen use ESC key

Press AMRT key

Set : End keyPM1 : Enter 1 press exe; you may enter any particular monthPM2 : Enter 25 Press exe; you may enter any particular month, but should be greater than PM1N : 36 press exe; (3 years and 12 months in a year)I% : 2 press exe; the interest %PV : 10000 press exe; the principal amountPMT : enter -286.43 press exe; the PMT can be worked out by using CMPD keyFV : 0 press exe; should be left blankP/Y : 12 press exe; payments in a yearC/Y : 12 press exe; compounding in a year

BAL : SOLVE key : Answer shall be 3119.29

INT : SOLVE Key : Answer shall be -16.666

PRN : SOLVE Key : Answer shall be -269.76

INT : SOLVE key : Answer shall be -280.04

- 7


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Explanation

Operation

Day or date calculation

The days mode helps you to calculate the number of days from any specific date to anyspecific date.

The following simulation is possible

If days and d1 is known then d2 can be calculatedIf days and d2 is known then d1 can be calculatedIf d1 and d2 is known then days can be calculated

d1 is the first date and d2 is the date after the d1

D1 D2

Before entering the data following options are available

The option of setting the day as 360 or 365 is availableMode of entering the date as DMY or MDY, the same can be selected in setup key

Let us see the practical aspect of the same

Press DAYS key and using the scroll key enter the following

By leaving any one variable blank and filling the other two variables, we can find thethird variable.

The option of date format can be chosen either DDMMYYYY or MMDDYYYY from thesetup screen.

Set : 365

D1 : 30072004 i.e. July 30, 2004

D2 : 17052005 i.e. May 17, 2005Dys : press SOLVE key and the answer shall be 291 days

Days


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Explanation

Depreciation calculation

With the help of FC200 we can calculate the following four popular method ofcalculating the depreciation on fixed assets:

Depreciation means wear and tear of the assets due to its usage.

Straight Line Method (SL)Fixed Percentage Method (FP)Sum of Years Digit Method (SYD)Declining Method or written Down Value Method (WDV)

Straight Line Method= (P-S)/n P= Principal Value

S=Salvage value if anyN=Number of years

Fixed Percentage Method = (P-S) x FP P= Principal Value

S=Salvage value if anyN=Number of years

Sum of years Digit Method

First Year = N (P-S)Sum-of years

Second Year = N-1 (P-S)

Sum-of years

Third Year = N-2 (P-S)Sum-of years

.

.

Last Year = 1 (P-S)

Sum-of years

For our exam le N=5 and the sum of ears is 1+2+3+4+5=15

Declining method or WDV

Depreciation in First year = (P) x Depreciation rate

Second year and onwards= (Net book value) x Depreciation rate

Net book Value = (P-S-Accumulated depreciation)

Depreciation rate =


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Operation

The following setting values should be done (hypothetical values)

Press DEPR key and using the scroll key and EXE key press following values

N = 6 (life of assets in terms of years)I% = 25 (fixed rate of depreciation incase of Fixed percentage method)

= 200 (depreciation factor in case of Declining Method)PV = 12000 (Cost of the assets)

FV = 0 (residual value if any)j = 1 (year for which the depreciation is being calculated)

YR1 = 12 (number of months in the first year)*

*In the initial year of buying the assets it is quite possible that depreciation is allowedonly for part of the year in that case required number of months need to be entered.

You need to input I% only if you use FP or DB method of depreciation

With the help of FC200V the calculation for any years depreciation is possible also thefactor for

SL = SOLVE Key

SL = 2000RDV = 10000j = 1

RDV means the value afterdepreciation

FP = SOLVE Key

FP = 3000

RDV = 9000j = 1

RDV means the value after

depreciation

SYD = SOLVE Key

SYD = 3428.57

RDV = 8571.42j = 1

RDV means the value after

depreciation

DB = SOLVE Key

DB = 4000RDV = 8000

j = 1

RDV means the value afterdepreciationDont forget to change the I%=asfactor instead of Fixed percentage


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Explanation

Break even point analysis

This is a very common term used often by Finance Manager or Production Manager, apoint of sales or a point of quantities to sell where the company would break even orto ore specifically company would neither gain nor lose. The profit at such sales wouldbecome Nil or 0%.

This tool is very important for Managers as it suggest that company to break evenmust sell at least N number of quantities.

Lets see the calculation of Break even (quantities)

Break even (quantities)=Fixed Cost / (Selling Price(Unit)

Variable Cost(Unit)

)

Break Even (Values) = Break even (quantities) x Selling price (Unit)

For calculating the BE we need selling price per unit (PRC), variable cost per unit

(VCU), Fixed Cost (FC)

Using the FC200V

Press BEVN key and using the scroll key enter the following values

Press exe key at BEV and input the following Hypothetical data

Set : PRF / Quantities using exe key use appropriate options

PRF / ratio press exe key using again exe key select ant of the

following

1. PRF

2. r% or

B-even press exe key and using again exe key select any of

the following

1. quantities (QBE)

2. Sales (SBE)


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Operation

Using Exe key enter following

*In case the company wants to know how much quantities need to be sold for

achieving the profit (PRF) of say 10000, then after selecting PRF above enter the PRF /

r% as 10000 and then QBE and SBE can be calculated for a profit target of 10000

* the option can be used if company wants to know that how much quantities need to

be sold for achieving the profit % of say 10%, then after selecting r% above enter the

PRF / r% as 10 and then QBE and SBE can be calculated for a profit target of 10%.

Margin of Safety (MOS)

Margin of safety denotes that how much sales can be dropped before attaining the

losses. For example if sales are 120000 and SBE is 48000 then MOS shall be 0.60.

That denotes that sales from the present levels can be dropped by 60% before

company starts incurring losses.

Continuing from the last hypothetical figures where the SBE was 48000 and suppose

the actual sales are 120000 that means the actual sales are more than the Break even

sales of 48000. I.e. Margin of safety is 60%

By inputting any two values

third value can be calculated

DEGREE OF OPERATING LEVERAGE (DOL)

The extent to which a business uses fixed costs (compared to variable costs) in its

operations is referred to as "operating leverage." The greater the use of operatingleverage (fixed costs, often associated with fixed assets), the larger the increase inprofits as sales rise and the larger the increase in loss as sales fall.

Press Exe key on MOS

Input the sales SAL : 120000

SBE : 48000

MOS : 0.60

PRC = 100

VCU = 75

FC = 12000


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= Sales less Variable cost / sales less total cost

Degree of operating

leverage can be calculated if

we know the total sales, total

variable cost and the total

fixed cost.

DEGREE OF FINANCIAL LEVERAGE (DFL)

The degree of financial leverage (DFL) is defined as the percentage change inearnings per share [EPS] that results from a given percentage change in earningsbefore interest and taxes (EBIT), and is calculated as follows:

DFL = Percentage change in EPS divided by Percentage change in EBIT

This calculation produces an index number which if, for example, is 1.43, means that a

100 percent increase in EBIT would result in a 143 percent increase in earnings pershare

In simple terms the DFL means the impact of Interest expenses on the earnings of the

company

DEGREE OF COMBINED

LEVERAGE (DCL)

Combined leverage is the product of operating leverage and financial leverage.That is: DTL=DOL*DFLWhere: DTL=degree of total leverage.DOL=degree of operating leverage.

DFL=degree of financial leverage.

Application of total leverage

1. Degree of total leverage measures the percentage change in EPS that results from

a change in one percent in output.

Press Exe key on DOL

Input the sales SAL : 120000

VC : 90000

FC : 10000

DOL press solve key : 1.5

Press Exe key on DFL

EIT (earnings before Interest) :120000

ITR (Interest) : 9000

DFL press solve key : 1.081


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2. It assists in measuring the firms total risk.

Press Exe key on DCL

SAL (total sales) :120000

VC (Variable cost) : 90000

FC (Fixed Cost) : 10000

ITR (Interest) : 9000

DCL press Solve : 2.7272


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Statistical analysis

Before understanding the concept of Standard deviation, we must understand the

term Mean and Variance

Mean as a common meaning denotes the center and arithmetically represents the

average of the given population or sample data

Variance is a parameter that measures how dispersed a random variables probability

distribution is. For two random variables the one on the left is more dispersed than the

one on the right. It has a higher variance. In more common terminology we can say

that it measures the variability from the mean.

Variance can be of two types:

Population variance

Sample Variance

High vs. Low Variance

Example of Population variance

The population variance is the mean squared deviation from the population mean:

Here is an example of the variance formula in action.


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2

= Population Variance

= Mean


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Example of Sample variance

In practice population variance cannot be computed directly because the entire population

is not ordinarily observed. An analogous measure of variability may be determined with

sample data. This referred to as sample variance

Sample variance can be calculated in the similar way as Population variance except thatthe divisional factor is one number less than the total numbers i.e N

S2

=Sample variance =

X = Sample mean data

Standard Deviation

The standard deviation is the positive square root of the variance:

Population standard deviation:

Sample standard deviation:

Let us take the an example having one variable and calculate above said

Press Setup key and using the scroll key STAT: On/Off key Select On by

pressing EXE

Press STAT key and select type

1

)(12

=

=

n

xx

s

N

i

i

2 =

1- 1- Var

: exe

2- A + B X

: exe

3- _ + cX2

: exe

4- In X

: exe

5- e^X

: exe

6- a + b^X

: exe

7- a +X^B

: exe

8- 1/X

: exe

2)1(1 =

2)1(


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Example for 1- Var (single variable)

Press Stat and chose option from type 1-var by pressing exe key and enter the

following data using cursor and exe key

X freq

1 10 1

2 12 1

3 14 1

4 16 1

5 18 1

6 20 1

7 18 1

8 16 1

9 14 1

10 12 1

Press AC key and Shift S-Menu and by selecting the appropriate digit following options

available

Press 1 we get the table __ above

Press 2 we get the option of more data entry

Press 3 we get the option of editing the data

Press 4 we get the option of 1. x2 2. x

Press 1 and below screen appears

Sum of variable x

Press Exe

Press 2 and below screen appears

1. Type 2. Data

3. Edit 4. Sum

5. Var 6. MinMax

x2

0

x2

2340

x

150

x

0

Please note for all calculation Press AC key and Shift S-menu key and then


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Press exe


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Press AC-Shift-S-Menu and option 5, we get the following screen

RGB 204,255,153

Press 1:

Press exe Press exe

Press AC Shift S-Menu- 5- 2

Press exe

Press AC Shift S-Menu- 5- option 3

Press exe

Press AC Shift S-Menu- 5- option 4

Press exe

Press AC Shift S-Menu- 6- we get options of 1: minX and maxX

Press 1

Press exe

1: n 2: X

3: Xn 4: xn-1

n

10

n

0

0 15

Xn

0

Xn

3

Xn-1

0

Xn-1

3.162277

minX

0

minX

10


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Press AC Shift S-Menu- 6- we get options of 2

Press exe

In case of two variables the frequency column is used for another variable and the calculationis based on the following formula and the formula shall be based on the following shortcut of

variance and Standard Deviation.

= X - ( X)/n

n

******

maxX

0

maxX

20


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Commands when linear regression calculation (A+ BX) is selected

When linear regression calculation is selected the calculation is performed by the followingmodel is selected i.e. a + b X and the calculation are done based on the following:


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Using FC200V following calculation is possible

Steps in case of 1-variable Formula Details

Shift (S-menu) 5-Var 1 n Number of variables

Shift (S-menu) 5-Var 2 Mean of the variables (x data)

Shift (S-menu) 4-sum 2 X Sum of the variables (x data)

Shift (S-menu) 4-sum 1 X Sum of squares of variables ( x data)

Shift (S-menu) 5-Var 3 Xn

Population standard deviation (x data)

Shift (S-menu) 5-Var 4 Xn-1Sample standard deviation (x data)

Shift (S-menu) 6-MinMax 1 minX Minimum of x values

Shift (S-menu) 6-MinMax 2 maxX Maximum of x values

Steps in case of more than 1variable, in addition to above

Formula Details

Shift (S-menu) 4-sum 4 y Mean of the variables ( y data)

Shift (S-menu) 4-sum 3 y Sum of squares of variables ( y data)

Shift (S-menu) 4-sum 5 xy Sum of products of x data and y data

Shift (S-menu) 4-sum 7 Xy Sum of x2 data X y data

Shift (S-menu) 4-sum 6 X Sum of cubes of x data

Shift (S-menu) 4-sum 8 X Sum of bi-squares of x data

Shift (S-menu) 5-Var 5 Mean of variables (y data)

Shift (S-menu) 5-Var 6 yn

Population standard deviation (y data)

Shift (S-menu) 5-Var 7 yn-1

Sample standard deviation (y data)

Shift (S-menu) 6-MinMax 3 minY Minimum if y values

Shift (S-menu) 6-MinMax 4 maxY Maximum of y values

Shift (S-menu) 7-Reg 1 A Regression coefficient constant term A

Shift (S-menu) 7-Reg 2 B Regression coefficient term b

Shift (S-menu) 7-Reg 3 r Correlation coefficient r

Shift (S-menu) 7-Reg 4 Estimated value of

Shift (S-menu) 7-Reg 5 Estimated value of


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Example in the case of A+BX

X 2 3 4 5 6 7 8 9

Y 12 13 14 15 16 17 18 19

Steps in case of 1-variable Formula Result

Shift (S-menu) 5-Var 1 n 8

Shift (S-menu) 5-Var 2 5.5

Shift (S-menu) 4-sum 2 x 44

Shift (S-menu) 4-sum 1 X 284


2.291287

Shift (S-menu) 5-Var 4 Xn-12.449489

Shift (S-menu) 6-MinMax 1 minX 2

Shift (S-menu) 6-MinMax 2 maxX 9

Shift (S-menu) 4-sum 4 y 124


Shift (S-menu) 4-sum 5 xy 724

Shift (S-menu) 4-sum 7 Xy 4864





2.291287

Shift (S-menu) 5-Var 7 yn-12.449489

Shift (S-menu) 6-MinMax 3 minY 12

Shift (S-menu) 6-MinMax 4 maxY 19

Shift (S-menu) 7-Reg 1 A 10

Shift (S-menu) 7-Reg 2 B 1

Shift (S-menu) 7-Reg 3 r 1

Shift (S-menu) 7-Reg 4 Estimated value y=3 =-7

Shift (S-menu) 7-Reg 5

Estimated value x=3 =13


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Commands when other types of Regression calculation(s) are selected

1. Quadratic Regression (_CX), Model equation y= A+BX+CX

2. Logarithmic Regression (In X), model equation y= A+BInX

3. Exponential Regression (e^X), model equation y= AeBX


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4. Power Regression (A*X^B), model equation y= AXB

5. Inverse Regression (1/X), Model equation y= A+B/X


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Example in case of quadratic regression equation

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19

COMMANDS Formula Result

Shift (S-menu) 5-Var 1 N 8

Shift (S-menu) 5-Var 2 9




4.582575695












4.993746089

Shift (S-menu) 5-Var 7 yn-1 5.338539126



Shift (S-menu) 7-Reg 1 A 1.75

Shift (S-menu) 7-Reg 2 B 0.70833333

Shift (S-menu) 7-Reg 3 C 0.02083333

Shift (S-menu) 7-Reg 4 If Y=3 then = 1.68154169


If Y=3 then 2= -5.6815416

Shift (S-menu) 7-Reg 6 If X=2 then = 3.25


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Example in the case of Logarithmic Regression (In X), model equation y= A+BInX

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19







4.582575695












4.993746089

Shift (S-menu) 5-Var 7 yn-1 5.338539126



Shift (S-menu) 7-Reg 1 A -4.106502688

Shift (S-menu) 7-Reg 2 B 7.111677003

Shift (S-menu) 7-Reg 3 r 0.9370197279


Shift (S-menu) 7-Reg 5 If x=3 then = 3.706473061


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Example in the case of Exponential Regression (e^X), model equation y= AeBX

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19







4.582575695












4.993746089




Shift (S-menu) 7-Reg 1 A 2.964238069

Shift (S-menu) 7-Reg 2 B 0.1218549797

Shift (S-menu) 7-Reg 3 R 0.9778589787



If x=3 then

= 4.27243945


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Example in the case of ab Exponential Power Regression (A*b^x), model equation

y= ABX

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19







4.582575695


Shift (S-menu) 6-MinMax 1 MinX 2

Shift (S-menu) 6-MinMax 2 MaxX 16




Shift (S-menu) 4-sum 7 yX 11696




Shift (S-menu) 5-Var 6 Yn

4.993746089




Shift (S-menu) 7-Reg 1 A 2.964238069

Shift (S-menu) 7-Reg 2 B 1.129590276

Shift (S-menu) 7-Reg 3 R 0.9778589787




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Example in the case of Power Regression (A*x^b), model equation y= AXB

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19


Shift (S-menu) 5-Var 1 N 8





4.582575695












4.993746089




Shift (S-menu) 7-Reg 1 A 1.550191285

Shift (S-menu) 7-Reg 2 B 0.8643765905

Shift (S-menu) 7-Reg 3 R 0.9959314857




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Example in the case of Inverse Regression (1/X), Model equationy= A+B/X

X 2 4 6 8 10 12 14 16

Y 3 5 7 9 11 13 15 19







4.582575695












4.993746089




Shift (S-menu) 7-Reg 1 A 15.2498118

Shift (S-menu) 7-Reg 2 B -29.43384607

Shift (S-menu) 7-Reg 3 r -0.8098270919




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Bond (Annualized Yield or Yield to Maturity)

The customary way of calculating the yield on Bonds purchased from the market is to typically

finding the Internal Rate of Return (IRR)

To understand Bond we must understand the complete terminology of the Bonds, e.g.

Coupon Rate = CPN = rate of interest payable on the face value of the Bonds

Purchase price = PRC = Price at which these bonds are available in the market

Redemption value = RDV = Price at which maturity value is paid back to bondholders

Term = n = Period of the bond, it can be either Fixed or can be derived from two dates

Yield = YLD = the effective rate of interest or YTM.

Example

A bond sold in the market at discount of 5% (face value-100, coupon rate-4%) and has a termperiod of 5 years. Find out its effective return?

An investor to this Bond shall enjoy following benefits

Period Cash flow

Year 0 -95

Year 1 04Year 2 04

Year 3 04Year 4 04

Year 5 104* (*Investor would get the Principal amount also in addition to Interest)

Equate the present value of all Cash flows to Zero and using the trial and error method findout its Yield, using a discount factor of 5%, we get following

CF0(5%, 1st year)+CF1(5%, 2nd Year)+CF2(5%, 3rd Year)+CF3(5%, 4th year)+CF5(5%, 5th Year)=0

= (-95*0.9523)+(4*0.90702)+(4*0.86384)+(4*0.82270)+(104*0.78353)

=1.39

Similarly using the Discount factor at 5.25% we get the net present value as -0.374649

To be more precise the YTM shall be 5.16% where the discounted cash flows shall be nearlyequal to Zero.


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Operation: Press BOND key and using scroll and exe key enter the following data:

The interest option can be selected either Annual or Semi annual and also the

period of bond can be either fixed or term Fixed period bonds shall give the option of putting two different dates as

purchase date and maturity date Term period bond give the option of only putting the number of years as the

life of the bond

If the Coupon rate is 4% and the Redemption price if 100 and to get the Yield of 8% what

should be the purchase price of the bond in the market?

The purchase price shall be 84.03 in the market to get the yield of 8% in the bond the Interest

accrued on such bond shall be zero and the purchase price including interest shall be 84.03only

Bond CalcSet: Annual / Term*N= 5: Press exeRDV=100: press exeCPN= 4: Press exePRC=-95: press exe

YLD=Solve key

YLD=5.159986152

Bond CalcSet: Annual / Term*N= 5: Press exeRDV=100: press exeCPN= 4: Press exePRC=Solve KeyYLD=8: Press exe

PRC= -84.02915985INT= 0

CST= =-84.02915985


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Defining the setup keys

The initial setup for various key is as per following table and to change the settings value the

procedure defined in the next pages shall be followed:

1. Payment Mode: Used in CMPD and AMRT Modes, the calculation of interest isdependant on the payment mode i.e. in advance (begin) or after the completion ofmonth (end), for choosing the correct option following is the procedure:

Press Setup key and using scroll key select the following menu

Exe Choose 1

2. Date Mode: Used in SMPL, DAYS and BOND Modes, the days in the year can be 365 or

360 days depending upon the usage and practice, the same can changed as followed

Exe Choose 1

3. DN: Used in CMPD mode, these settings specifies whether Simple Interest (SI) orCompound Interest (CI) is to be used for partial months to change the settings

Exe Choose 2

4. Periods: Used in BOND mode , Year: Annual or Semi annual coupons payment peryear, the bond can have the payment of interest either annually or semi annually. Thesettings can be configured as follows:

Exe Choose 2

Payment: EndPayment

1. Begin2. End

Payment: Begin

Date Mode: 365 Date Mode: 360Date Mode

1 3602 365

DN: CI DN: SIDN

1: CI2: SI

Periods/Y: Annu Date Mode: 365Periods/year

3 Annual4 Semi


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5. Bond date: used in BOND mode only, Date in case of Bonds purchased the same canbe either having a fixed term or two dates can specified, i.e. Date of purchase and the

date of maturity. The initial settings can be modified as follows:

Exe Choose2

6. Date Input: MDY: used in case of DAYS and BOND mode only, the dates can be input

either of the following way, Month/Day/Year (MDY) or Date/Month/Year (DMY), theinitial settings of MDY can be modified as follows:

Exe Choose2

7. PRF/Ratio: PRF, used in the case BEVN mode only, Profit or profit percentage can be

specified, the initial settings can be modified as follows:

Exe Chose2

8. B-Even : Quantity, used in the case BEVN mode only and the break even can be

calculated either in term of quantity or Sales amount, the initial settings of quantity canbe modified as follows:

Exe Chose2

9. Digit Separator : used in all modes and is an option used for making the digit appearing

as

123456 Superscript mode 123456123456 Subscript mode 123,456

123456 Separator Off 123456

10 Angle, Fix, Sci and Norm modes are used in all modes and the calculations and are easy

to understand and modify the initial settings.

Bond date: Date Bond Date5 Date

6 Term

Bond Date: Term

PRF/Ratio: PRF

Date Mode: 365Date Input

1 MDY

2 DMYDate In ut: MDY

PRF / Ratio1 PRF2 R%

PRF/Ratio: r%

B-Even: SalesB- Even1 Quantity2 Sales

B-Even: Quantity


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11. Stat: on ,used is STAT mode only and is an application which is used when the

statistical calculations are to be performed then the stat mode can be turned on or offby following the following procedure

Exe Choose2 STAT: OffSTAT1. On2. Off

STAT: On

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