Casio CFX-9970G User manual

Chapter
19
Financial Calculations
19-1 Before Performing Financial Calculations
19-2 Simple Interest Calculations
19-3 Compound Interest Calculations
19-4 Investment Appraisal
19-5 Amortization of a Loan
19-6 Conversion between Percentage Interest Rate and
Effective Interest Rate
19-7 Cost, Selling Price, Margin Calculations
19-8 Day/Date Calculations

320
19-1 Before Performing Financial Calculations
The Financial Mode provides you with the tools to perform the following types of
financial calculations.
• Simple interest
• Compound interest
• Investment appraisal (Cash Flow)
• Amortization
• Interest rate conversion (annual percentage rate and effective interest rate)
• Cost, selling price, margin
• Day/date calculations
uu
uu
uGraphing in the Financial Mode
After performing a financial calculation, you can use 6(GRPH) to graph the
results as shown below.
• Pressing !1 (TRCE) 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 edisplays PV, SI, and SFV. Pressing ddisplays the
same values in reverse sequence.
• Zoom, Scroll, Sketch, and G-Solve cannot be used in the Financial Mode.
• In the Financial Mode, horizontal lines are blue and vertical lines are red.
These colors are fixed and cannot be changed.
• The present value is positive when it represents receipt of money, and a
negative value when it represents a payment.
• 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.
uu
uu
uSet up screen settings
Note the following points regarding set up screen settings whenever using the
Financial Mode.
• The following graph set up screen settings are all turned off for graphing in the
Financial Mode:Axes, Grid, Dual Screen.
P.6
P.7

321
• 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).
• 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
kEntering the Financial Mode
On the Main Menu, select the TVM icon to enter the Financial Mode. When you
do, the Financial 1 screen appears on the display.
Financial 1 screen Financial 2 screen
•{SMPL}/{CMPD}/{CASH}/{AMT}/{CNVT}/{COST}/{DAYS} ... {simple interest}/
{compound interest}/{cash flow}/{amortization}/{conversion}/{cost, selling
price, margin}/{day/date} calculation
Before Performing Financial Calculations 19 - 1
P.6

322
19-2 Simple Interest Calculations
This calculator uses the following formulas to calculate simple interest.
365-day Mode
SI' = n
365× PV × i
SI' = n
360× PV × i
I%
100
i =
I%
100
i =
SI : simple interest
n: number of simple
360-day Mode interest periods
PV : present value
I%: periodic interest rate
SFV: simple future value
SI = –SI'
SFV = –(PV +SI')
Press 1(SMPL) from the Financial 1 screen to display the following input screen
for simple interest calculation.
n ......................number of simple interest periods (days)
I% ................ annual interest rate
PV .................. present value
•{SI}/{SFV} ... calculates {simple interest}/{simple future value}
Example What would the interest amount and principal plus interest be
for a loan of $1,500 borrowed for 90 days at an annual rate of
7.25%?
Use the 360-day mode and two decimal places.
In the set up screen, specify “360” for Date Mode and “Fix2” for Display and then
press J.
Perform the following key operation from the input screen.
jaw
h.cfw
-bfaaw
1(SI)
P.7
P.6

323
Now you can perform the following key operation to return to the input screen and
then display the principal plus interest.
1(REPT) (Returns to the input screen)
2(SFV)
You can also press 6(GRPH) to draw a cash flow graph.
6(GRPH)
The left side is PV, while the right side is SI and SFV. The upper part of the graph
is positive (+), while the bottom part is negative (–).
• V-Window values vary in accordance with simple interest conditions.
Press J(or !6 (G↔T)) to return to the input screen.
Press Jagain to return to the Financial 1 screen.
Simple Interest Calculations 19 - 2

324
19-3 Compound Interest Calculations
This calculator uses the following standard formulas to calculate compound
interest.
uu
uu
uFormula I
PV+PMT u + FV
i(1+ i)
n
(1+ i)
n
(1+ i u S)[(1+ i)
n
–1]1= 0
i = 100
I％

Here:
PV= –(PMT u+ FV u )
β
α
FV= –
β
PMT u + PV
α
PMT= –
β
PV + FV u
α
n =
log
{ }
log(1+ i)
(1+ i S ) PMT+PVi
(1+ i S ) PMT–FVi
i
(
1+i
)
n
(1+ i u S)[(1+ i)
n
–1]
=
α
(1+ i)
n
1
=
β
F(i) = Formula I
+ (1+ i S)[n(1+ i)
–n–1
]+S[1–(1+ i)
–n
]
+ FV–n(1+ i)
–n–1
ii
PMT (1+ i S)[1– (1+ i)
–n
]
F(i)'= –
[]
uu
uu
uFormula II (I% = 0)
PV + PMT × n + FV = 0
Here:
PV = – (PMT un + FV )
FV = – (PMT un + PV )
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 beginning of term
S= 1 assumed for end of term

325
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.
I%' = I%
(1+ ) –1
[C / Y ]
[P / Y ]
100 × [C / Y ]
{ }
×100
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.
Press 2(CMPD) in the Financial 1 screen to display the input screen for
compound interest calculation.
n..................... number of compound periods
I% ................... annual interest rate
PV .................. present value (loan amount in case of loan; balance in case
of savings)
Compound Interest Calculations 19 - 3

326
19 - 3 Compound Interest Calculations
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
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.
kk
kk
kCompound Interest Examples
This section shows how compound interest calculations can be used in a variety
of applications.
uu
uu
uSavings (standard compound interest)
Input Condition: Future value is greater than present value.
Formula Representation of Input Condition: PMT = 0
|PV| < |FV|
Example Calculate the interest rate required to increase a principal of
$10,000 to $12,000 in three years, when compounding is
performed semiannually.
Perform the following key operation from the input screen.
d*bcw(Input n= 3 ×12.)
c
-baaaaw(PV = –10,000)
aw
bcaaaw(FV = 12,000)
bw
cw(Semiannual compounding)
2(I%)

327
Now you can press 6to draw a cash flow graph.
6(GRPH)
The left side is PV, while the right side is FV. The upper part of the graph is
positive (+), while the bottom part is negative (–).
uu
uu
uInstallment savings
Input Condition: Future value is greater than the total of payments.
Formula Representation of Input Condition:
PMT and FV have different signs (positive, negative) when PV = 0.
–FV < n×PMT when FV > 0
–FV > n×PMT when FV < 0
Example Calculate the interest rate required to have a $2,500 balance in
an installment savings account in two years when $100 is
deposited each month and interest is compounded semiannu-
ally.
Perform the following key operation from the input screen.
c*bcw(Input n= 2 ×12.)
c
aw(PV = 0)
-baaw(PMT = –100)
cfaaw(FV = 2,500)
bcw(Monthly installment)
cw(Compounding every six months)
2(I%)
uu
uu
uLoans
Input Condition: Total of payments is greater than loan amount.
Formula Representation of Input Condition:
PMT and PV have different signs (positive, negative) when FV = 0.
–PV > n×PMT when PV > 0
–PV < n×PMT when PV < 0
Compound Interest Calculations 19 - 3

328
Example Calculate the interest rate required to repay a $2,300 balance
on a loan in two years paying back $100 per month, when
interest is compounded monthly.
Perform the following key operation from the input screen.
c*bcw(Input n= 2 ×12.)
c
cdaaw(PV = 2,300)
-baaw(PMT = –100)
aw(FV = 0)
bcw(Monthly installment)
(Monthly compounding)
2(I%)
uu
uu
uLoan when final installment is greater than other installments
Input Condition: Total of equal amount payments is greater than the difference
between the loan amount and final payment amount.
Formula Representation of Input Condition:
PV,PMT, FV do not equal zero.
PV + FV > – n×PMT when FV > PV
PV + FV < – n×PMT when FV < PV
Example Calculate the interest rate required to repay a $2,500 balance
on a loan in two years (24 installments) paying back $100 per
month and a final $200 installment, when interest is com-
pounded monthly.
Perform the following key operation from the input screen.
c*bcw(Input n= 2 ×12.)
c
cfaaw(PV = 2,500)
-baaw(PMT = –100)
-caaw(FV = –200)
bcw(Monthly installment)
(Monthly compounding)
2(I%)
19 - 3 Compound Interest Calculations
The value you input for P/Y (the
number of installment periods per
year) is also automatically input for
C/Y (the number of compounding
periods per year). You can input
another value for C/Y if you want.