Casio ALGEBRA FX 2.0 Plus User manual

Financial Calculation (TVM)
2-1 Before Performing Financial Calculations
2-2 Simple Interest
2-3 Compound Interest
2-4 Cash Flow (Investment Appraisal)
2-5 Amortization
2-6 Interest Rate Conversion
2-7 Cost, Selling Price, Margin
2-8 Day/Date Calculations
2-9 Depreciation
2-10 Bonds
2-11 TVM Graph
2
Chapter
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2-1 Before Performing Financial Calculations
kk
kk
kTVM Mode
On the Main Menu, select the TVM icon.
Entering the TVM Mode displays the Financial screen like the one shown below.
Financial 1 screen Financial 2 screen
•1(SMPL) .... Simple interest
•2(CMPD) ... Compound interest
•3(CASH) .... Cash flow (investment appraisal)
•4(AMT) ...... Amortization
•5(CNVT) .... Interest rate conversion
•6(g)1(COST) ... Cost, selling price, margin
2(DAYS) ... Day/date calculations
3(DEPR) ... Depreciation
4(BOND) ... Bonds
5(TVMG) ... TVM (compound interest simulation) graph
2-1-1
Before Performing Financial Calculations
* The above shows the ALGEBRA
FX 2.0 PLUS screen.

20010101
kk
kk
kSET UP Items
uu
uu
uPayment
•{BGN}/{END}........ Specifies {beginning of the period} / {end of the period} payment
uu
uu
uDate Mode
•{365}/{360}......... Specifies calculation according to a {365-day} / {360-day} year
uu
uu
uPeriods/YR. (Bond)
•{Annual}/{SEMI}... Indicates an {annual} / {semi-annual} period
Note the following points regarding SET UP screen settings whenever using the Financial
Mode.
•Drawing a financial graph while the Label item is turned on, displays the label CASH for the
vertical axis (deposits, withdrawals), and TIME for the horizontal axis (frequency). Axis
labels do not appear on the TVM graph.
•The number of display digits applied in the Financial Mode is different from the number of
digits used in other modes. The calculators automatically reverts to Norm 1 whenever you
enter the Financial Mode, which cancels a Sci (number of significant digits) or Eng
(engineering notation) setting made in another mode.
kk
kk
kGraphing in the TVM Mode
After performing a financial calculation, you can use 6(GRPH) to graph the results as shown
below.
•Pressing 1(TRACE) while a graph is on the display activates Trace, which can be used to
look up other financial values. In the case of simple interest, for example, pressing e
displays PV, SI, and SFV. Pressing ddisplays the same values in reverse sequence.
•Zoom, Scroll, and Sketch cannot be used in the Financial Mode.
•Whether you should use a positive or a negative value for the present value (PV) or the
purchase price (PRC) depends on the type of calculation you are trying to perform.
•Note that graphs should be used only for reference purposes when viewing TVM Mode
calculation results.
•Note that calculation results produced in this mode should be regarded as reference values
only.
•Whenever performing an actual financial transaction, be sure to check any calculation results
obtained using this calculator with against the figures calculated by your financial institution.
2-1-2
Before Performing Financial Calculations

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2-2 Simple Interest
This calculator uses the following formulas to calculate simple interest.
uu
uu
uFormula
365-day Mode
SI' = n
365 × PV × i
SI' = n
360 × PV × i
I%
100
i =
I%
100
i =
SI :interest
n:number of interest
360-day Mode periods
PV :principal
I%:annual interest
SFV :principal plus interest
SI = –SI'
SFV = –(PV +SI')
Press 1(SMPL) from the Financial 1 screen to display the following input screen for simple
interest.
1(SMPL)
n.................................. number of interest periods (days)
I%............................... annual interest rate
PV ............................... principal
After configuring the parameters, press one of the function keys noted below to perform the
corresponding calculation.
•1(SI) ....... Simple interest
•2(SFV) ... Simple future value
2-2-1
Simple Interest

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• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
•1(REPT) ... Parameter input screen
•6(GRPH) ... Draws graph
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation
results along the graph.
Each press of ewhile trace is turned on cycles the displayed value in the sequence:
present value (PV) →simple interest (SI) →simple future value (SFV). Pressing dcycles
in the reverse direction.
Press ito turn off trace.
Press iagain to return to the parameter input screen.
2-2-2
Simple Interest

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2-3 Compound Interest
This calculator uses the following standard formulas to calculate compound interest.
uu
uu
uFormula I
PV+PMT ×+ FV
i(1+ i)
n
(1+ i)
n
(1+ i × S)[(1+ i)
n
–1]1= 0
i = 100
I %
Here:
PV= –(PMT ×+ FV ×)
β
α
FV= –
β
PMT × + P
V
α
PMT= –
β
PV + FV ×
α
n =
log
{ }
log(1+ i)
(1+ i S ) PMT+PVi
(1+ i S ) PMT–FVi
i
(
1+ i
)
n
(1+ i × S)[(1+ i)n–1]
=
α
(1+ i)n
1
=
β
F(i) = Formula I
+ (1+ i S)[n(1+ i)–n–1]+S
[
– nFV(1+ i)–n–1
ii
PMT (1+ i S)[1– (1+ i)–n]
F(i) = –
[
+S [1–(1+ i)–n]
]
uu
uu
uFormula II (I% = 0)
PV + PMT × n + FV = 0
Here:
PV = – (PMT × n + FV )
PV :present value
FV :future value
PMT :payment
n:number of compound periods
I % :annual interest rate
iis calculated using Newton’s Method.
S= 0 assumed for end of term
S= 1 assumed for beginning of term
2-3-1
Compound Interest
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FV = – (PMT × n + PV )
n
PMT = –PV + FV
PMT
n = – PV + FV
• A deposit is indicated by a plus sign (+), while a withdrawal is indicated by a minus sign (–).
uu
uu
uConverting between the nominal interest rate and effective interest rate
The nominal interest rate (I% value input by user) is converted to an effective interest rate
(I%') when the number of installments per year (P/Y ) is different from the number of
compound interest calculation periods (C/Y ). This conversion is required for installment
savings accounts, loan repayments, etc.
P/Y:installment
periods per year
C/Y:compounding
periods per year
When calculating n, PV, PMT, FV
The following calculation is performed after conversion from the nominal interest rate to the
effective interest rate, and the result is used for all subsequent calculations.
i = I%'÷100
When calculating I%
After I% is obtained, the following calculation is performed to convert to I%'.
I%' = I%
(1+ ) –1
[C / Y ]
[P / Y ]
100
{ }
×[C / Y ]×100
P/Y:installment
periods per year
C/Y:compounding
periods per year
The value of I%' is returned as the result of the I% calculation.
2-3-2
Compound Interest
I%' = I%
(1+ ) –1
[C / Y ]
[P / Y ]
100 × [C / Y ]
{ }
×100
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Press 2(CMPD) from the Financial 1 screen to display the following input screen for
compound interest.
2(CMPD)
n.................................. number of compound periods
I%............................... annual interest rate
PV ............................... present value (loan amount in case of loan; principal in case
of savings)
PMT ............................ payment for each installment (payment in case of loan;
deposit in case of savings)
FV ............................... future value (unpaid balance in case of loan; principal plus
interest in case of savings)
P/Y.............................. installment periods per year
C/Y.............................. compounding periods per year
Important!
Inputting Values
A period (n) is expressed as a positive value. Either the present value (PV ) or future value
(FV) is positive, while the other (PV or FV ) is negative.
Precision
This calculator performs interest calculations using Newton’s Method, which produces
approximate values whose precision can be affected by various calculation conditions.
Because of this, interest calculation results produced by this calculator should be used
keeping the above limitation in mind or the results should be verified.
2-3-3
Compound Interest

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After configuring the parameters, press one of the function keys noted below to perform the
corresponding calculation.
•1(n) ............ Number of compound periods
•2(I%).......... Annual interest rate
•3(PV) ......... Present value (Loan: loan amount; Savings: balance)
•4(PMT) ....... Payment (Loan: installment; Savings: deposit)
•5(FV) .......... Future value (Loan: unpaid balance; Savings: principal plus interest)
•6(AMT) ....... Amortization screen
•An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function keys to maneuver between calculation result screens.
•1(REPT) ..... Parameter input screen
•4(AMT) ....... Amortization screen
•6(GRPH) .... Draws graph
After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation
results along the graph.
Press ito turn off trace.
Press iagain to return to the parameter input screen.
2-3-4
Compound Interest

20010101
2-4 Cash Flow (Investment Appraisal)
This calculator uses the discounted cash flow (DCF) method to perform investment appraisal
by totalling cash flow for a fixed period. This calculator can perform the following four types
of investment appraisal.
•Net present value (NPV )
•Netfuture value (NFV )
•Internal rate of return (IRR)
•Pay back period (PBP)
A cash flow diagram like the one shown below helps to visualize the movement of funds.
CF0
CF1
CF2CF3CF4
CF5CF6
CF7
With this graph, the initial investment amount is represented by CF0. The cash flow one year
later is shown by CF1, two years later by CF2, and so on.
Investment appraisal can be used to clearly determine whether an investment is realizing
profits that were originally targeted.
uNPV
NPV = CF0+ + + + … +
(1+ i)
CF1
(1+ i)2
CF2
(1+ i)3
CF3
(1+ i)n
CFn
i = 100
I %
n: natural number up to 254
uNFV
NFV =NPV × (1 + i )
n
uIRR
0 = CF 0 + + + + … +
(1+ i)
CF
1
(1+ i)
2
CF 2
(1+ i)
3
CF 3
(1+ i)
n
CF n
In this formula, NPV = 0, and the value of IRR is equivalent to i×100. It should be noted,
however, that minute fractional values tend to accumulate during the subsequent
calculations performed automatically by the calculator, so NPV never actually reaches
exactly zero. IRR becomes more accurate the closer that NPV approaches to zero.
2-4-1
Cash Flow (Investment Appraisal)