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
20010101

20010101
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

20010101
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

20010101
• 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

20010101
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
20011201

20010101
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
20011101

20010101
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

20010101
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)

20010101
uu
uu
uPBP
PBP is the value of nwhen NPV >0 (when investment can be recovered).
• Press 3(CASH) from the Financial 1 screen to display the following input screen for Cash
Flow.
3(CASH)
I%............................... interest rate (%)
Csh .............................. list for cash flow
If you have not yet input data into a list, press 5('LIST) and input data into a list.
After configuring the parameters, press one of the function keys noted below to perform the
corresponding calculation.
•1(NPV) ......... Net present value
•2(IRR) .......... Internal rate of return
•3(PBP) ......... Pay back period
•4(NFV) ......... Net future value
•5('LIST) ..... Inputs data from a list
•6(LIST) ......... Specifies a list for data input
• 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
2-4-2
Cash Flow (Investment Appraisal)
20011101

20010101
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.
2-4-3
Cash Flow (Investment Appraisal)

20010101
2-5 Amortization
This calculator can be used to calculate the principal and interest portion of a monthly
installment, the remaining principal, and amount of principal and interest repaid up to any
point.
uu
uu
uFormula
;;;
;;;;;
;;;;;;;
;;;;;;;;;
;;;;;;;;;;;
;;;;;;;;;;;;
;;;;;;;;;;; ;;;;;;;;; ;;;;;;; ;;;;; ;;;
;;
;;;
;;;;
;;;;
;;;
;
;;;;;
;
;;;
;
;
;;;
;
;
;;;
;
;
;;;
;
;
;;;
;
;
;;;
;
;
;;;
;
;
;;;
;
;;;;;
;;;
;;;;;
;;;;;; ;;;;;; ;;;; ;;
b
a
d
e
c
12 mn
a: interest portion of installment PM1 (INT)
b: principal portion of installment PM1 (PRN)
c: balance of principal after installment PM2 (BAL)
d: total principal from installment PM1 to payment of installment PM2 (ΣPRN)
e: total interest from installment PM1 to payment of installment PM2 (ΣINT )
*a+ b= one repayment (PMT)
a: INT PM1 =I BAL PM1–1 ×i I ×(PMT sign)
b: PRN
PM1 =PMT +BAL PM1–1 ×i
c: BAL
PM2 =BAL PM2–1 + PRN PM2
d:
Σ
PRN =PRN PM1 + PRN PM1+1 + … + PRN PM2
e:
Σ
INT =INT PM1 + INT PM1+1 + … + INT PM2
PM2
PM1
PM2
PM1
BAL0= PV (INT1= 0 and PRN1= PMT at beginning of installment term)
(Number of payments)
Amount of single payment
2-5-1
Amortization

20010101
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%') for installment loans where the number of installments per year is different from the
number of compound interest calculation periods.
I%' = I%
(1+ ) –1
[C / Y ]
[P / Y ]
100 × [C / Y ]
{ }
×100
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
Press 4(AMT) from the Financial 1 screen to display the following input screen for interest
rate conversion.
4(AMT)
PM1 ............................. first installment of installments 1 through n
PM2 ............................. second installment of installments 1 through n
n.................................. installments
I%............................... interest rate
PV ............................... principal
PMT ............................ payment for each installment
FV ............................... balance following final installment
P/Y.............................. installments per year
C/Y.............................. compoundings per year
2-5-2
Amortization

20010101
After configuring the parameters, press one of the function keys noted below to perform the
corresponding calculation.
•1(BAL) ......... Balance of principal after installment PM2
•2(INT) .......... Interest portion of installment PM1
•3(PRN) ......... Principal portion of installment PM1
•4(Σ INT) ....... Total interest paid from installment PM1 to installment PM2
•5(Σ PRN) ...... Total principal paid from installment PM1 to installment PM2
•6(CMPD) ...... Compound interest 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(CMPD) ...... Compound interest 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.
The first press of 1(TRACE) displays INT and PRN when n= 1. Each press of eshows
INT and PRN when n= 2, n= 3, and so on.
Press ito turn off trace.
Press iagain to return to the parameter input screen.
2-5-3
Amortization

20010101
2-6 Interest Rate Conversion
The procedures in this section describe how to convert between the annual percentage rate
and effective interest rate.
uu
uu
uFormula
EFF = n
APR/100
1+ –1 × 100
n
APR = 100
EFF
1+ –1 × n ×100
1
n
Press 5(CNVT) in the Financial 1 screen to display the following input screen for interest
rate conversion.
5(CNVT)
n....................................... number of compoundings
I%............................... interest rate
After configuring the parameters, press one of the function keys noted below to perform the
corresponding calculation.
•1('EFF) ... Converts annual percent rate to effective interest rate
•2('APR) ... Converts effective interest rate to annual percent rate
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function key to maneuver between calculation result screens.
•1(REPT) ... Parameter input screen
APR :annual percentage rate (%)
EFF :effective interest rate (%)
n:number of compoundings
2-6-1
Interest Rate Conversion
20011101

20010101
2-7 Cost, Selling Price, Margin
Cost, selling price, or margin can be calculated by inputting the other two values.
uu
uu
uFormula
CST = SEL 100
MRG
1–
SEL =
100
MRG
1–
CST
M
RG(%) = SEL
CST
1– × 100
Press 1(COST) from the Financial 2 screen to display the following input screen.
6(g)1(COST)
Cst ............................... cost
Sel ............................... selling price
Mrg .............................. margin
After configuring the parameters, press one of the function keys noted below to perform the
corresponding calculation.
•1(COST) .... Cost
•2(SEL) .......Selling price
•3(MRG) ...... Margin
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function key to maneuver between calculation result screens.
•1(REPT) ... Parameter input screen
CST :cost
SEL :selling price
MRG :margin
2-7-1
Cost, Selling Price, Margin

20010101
2-8 Day/Date Calculations
You can calculate the number of days between two dates, or you can determine what date
comes a specific number of days before or after another date.
Press 2(DAYS) from the Financial 2 screen to display the following input screen for day/
date calculation.
6(g)2(DAYS)
d1 ................................ date 1
d2 ................................ date 2
D................................. number of days
To input a date, first highlight d1 or d2. Pressing a number key to input the month causes an
input screen like the one shown below to appear on the display.
2-8-1
Day/Date Calculations
#The set up screen can be used to specify
either a 365-day or 360-day year for financial
calculations. Day/date calculations are also
performed in accordance with the current
setting for number of days in the year, but the
following calculations cannot be performed
when the 360-day year is set. Attempting to do
so causes an error.
(Date) + (Number of Days)
(Date) – (Number of Days)
#The allowable calculation range is January 1,
1901 to December 31, 2099.

20010101
Input the month, day, and year, pressing wafter each.
After configuring the parameters, press one of the function keys noted below to perform the
corresponding calculation.
•1(PRD) ........ Number of days from d1 to d2 (d2 – d1)
•2(d1+D)....... d1 plus a number of days (d1 + D)
•3(d1 – D)..... d1 minus a number of days (d1 – D)
• An error (Ma ERROR) occurs if parameters are not configured correctly.
Use the following function key to maneuver between calculation result screens.
•1(REPT) ...... Parameter input screen
360-day Date Mode Calculations
The following describes how calculations are processed when 360 is specified for the Date
Mode item in the SET UP screen.
• If d1 is day 31 of a month, d1 is treated as day 30 of that month is used.
• If d2 is day 31 of a month, d2 is treated as day 1 of the following month, unless d1 is day
30.
2-8-2
Day/Date Calculations

20010101
2-9 Depreciation
Any of the following four methods can be used to calculated depreciation.
uu
uu
uStraight-Line Method
The straight-line method calculates depreciation for a given period.
{Y–1}(PV–FV )
SL
1 = n12
u
(PV–FV )
SL
j = n
12–{Y–1}
({Y–1}G12)
(PV–FV )
n12
u
SL n+1 =
Depreciation for an item acquired part way through a year can be calculated by month.
uu
uu
uFixed Percentage Method
Fixed percentage method can be used to calculate depreciation for a given period, or to
calculate the depreciation rate.
100
I%
FP
j = (RDV j–1 + FV )×
100
{Y–1}I%
FP
1 = PV ×12
×
FP
n+1 = RDV n ({Y–1}G12)
RDV
1 = PV – FV – FP 1
RDV j = RDV j–1 – FP j
RDV n+1 = 0 ({Y–1}G12)
Depreciation for an item acquired part way through a year can be calculated by month.
SL j:depreciation charge for the jth
year
n:useful life in years
PV :original cost (basis)
FV :scrap value (salvage value)
j:year
Y–1:number of depreciable months
in first year
FPj:depreciation charge for the jth year
RDVj:remaining depreciable value at the
end of jth year
I % :depreciation rate
2-9-1
Depreciation