Casio ALGEBRA FX 2.0 User Manual
Financial Calculation (TVM)
Software for the
ALGEBRA FX2.0
1. Before Performing Financial Calculations
2. Simple Interest
3. Compound Interest
4. Cash Flow (Investment Appraisal)
5. Amortization
6. Interest Rate Conversion
7. Cost, Selling Price, Margin
8. Day/Date Calculations
9. Depreciation
10. Bonds
11. TVM Graph
2
1. Before Performing Financial Calculations
kk
k TVM Mode
kk
Installing the Financial Application on your ALGEBRA FX2.0 adds a TVM icon to the Main
Menu.
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
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kk
k SET UP Items
kk
uu
u Payment
uu
•{BGN}/{END} ........ Specifies {beginning of the period} / {end of the period} payment
uu
u Date Mode
uu
•{365}/{360} ......... Specifies calculation according to a {365-day} / {360-day} year
uu
u Periods/YR. (Bond)
uu
•{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
k Graphing in the TVM Mode
kk
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 T race, 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 d displays 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.
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2. Simple Interest
This calculator uses the following formulas to calculate simple interest.
uu
uFormula
uu
365-day Mode
360-day Mode
SI' =
SI' =
n
365
n
360
× PV × i
× PV × i
i =
i =
I%
100
I%
100
SI : interest
n : number of interest
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
•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
5
After drawing a graph, you can press 1 (TRACE) to turn on trace and read calculation results
along the graph.
Each press of e while trace is turned on cycles the displayed value in the sequence: present
value (PV) -> simple interest (SI) -> simple future value (SFV). Pressing d cycles in the
reverse direction.
Press i to turn off trace.
Press i again to return to the parameter input screen.
6
β
β
)
3. Compound Interest
This calculator uses the following standard formulas to calculate compound interest.
uu
uFormula I
uu
PV+PMT u + FV
Here:
(1+ i u S)[(1+ i)n–1] 1
n
i(1+ i)
(1+ i)
= 0
n
i =
I％
100
PV= –(PMT
PMT
V= –
PMT= –
log
n =
(1+ i u S)[(1+ i)n–1]
α
=
=
β
(1+ i)
F(i) = Formula I
F(i)= –
+S [1–(1+ i)
α
u
+ FV
u )
u
+ PV
α
PV + FV
β
u
α
(1+ i S ) PMT–FVi
{ }
(1+ i S ) PMT+PVi
log(1+ i)
n
i(1+ i
1
n
PMT
(1+ i S)[1– (1+ i)
[
–n
] – FV • n(1+ i)
]
ii
PV : present value
FV : future value
PMT : payment
n : number of compound periods
I
%
: annual interest rate
i is calculated using Newton’s Method.
S = 0 assumed for end of term
S = 1 assumed for beginning of term
–n
]
+ (1+ i S)[n(1+ i)
–n–1
–n–1
]
uu
uFormula II (I% = 0)
uu
PV + PMT × n + FV = 0
Here:
PV = – (PMT u n + FV )
FV = – (PMT u n + PV )
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PMT = –
n = –
• A deposit is indicated by a plus sign (+), while a withdrawal is indicated by a minus sign (–).
uu
uConverting between the nominal interest rate and effective interest rate
uu
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.
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%' =
PV + FV
n
PV + FV
PMT
[C / Y ]
I%' =
(1+ ) –1
{ }
I%
(1+ ) –1
{ }
100
I%
100 × [C / Y ]
[P / Y ]
[C / Y ]
[P / Y ]
×[C / Y ]×100
×100
P/Y: installment
periods per year
C/Y: compounding
periods per year
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.
Press 2(CMPD) from the Financial 1 screen to display the following input screen for compound interest.
• 2(CMPD)
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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; de-
posit 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
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.
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) ......... Prevent value
• 4(PMT) ...... Payment
• 5(FV) ......... Future value
• 6(AMT) ...... Amortization screen
(Loan: loan amount; Savings: balance)
(Loan: installment; Savings: deposit)
(Loan: unpaid balance; Savings: principal plus 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
• 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 i to turn off trace.
Press i again to return to the parameter input screen.
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