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.
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• 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
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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)
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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.

329
kk
kk
kSavings
uu
uu
uFuture value
Example Calculate the future value after 7.6 years for a principal of $500
and an interest rate of 6%, compounded annually.
Perform the following key operation from the input screen.
h.gw(n= 7.6 years)
gw(I= 6%)
-faaw(PV = –500)
aw(PMT = 0)
aw(FV = 0)
bw
bw(Annual compounding)
5(FV)
uu
uu
uPrincipal
Example Calculate the principal required at 5.5%, compounded monthly,
to produce a total of $20,000 in a year.
Perform the following key operation from the input screen.
b*bcw(Input n= 1 ×12.)
f.fw(I= 5.5%)
c
aw(PMT = 0)
caaaaw(FV = 20,000)
bw
bcw(Monthly compounding)
3(PV )
uu
uu
uCompound interest rate
Example Calculate the interest required, compounded monthly, to
produce a total of $10,000 in 10 years on an initial investment
of $6,000.
In the set up screen, specify “Begin” for Payment and then press J.
Compound Interest Calculations 19 - 3
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330
Perform the following key operation from the input screen.
ba*bcw(Input n= 10 ×12.)
c
-gaaaw(PV = –6,000)
aw(PMT = 0)
baaaaw(FV = 10,000)
bw
bcw(Monthly compounding)
2(I%)
uu
uu
uCompound interest period
Example Calculate the amount of time required to increase an initial
investment of $5,000 to a total of $10,000 at an annual rate of
4%, compounded monthly.
In the set up screen, specify “End” for Payment and then press J.
Perform the following key operation from the input screen.
c
ew(I% = 4)
-faaaw(PV = –5,000)
aw(PMT = 0)
baaaaw(FV = 10,000)
bw
bcw(Monthly compounding)
1(n)
uu
uu
uInstallment savings
Example Calculate (to two decimal places) the principal plus interest for
$250 monthly installments for five years at 6% annual interest,
compounded monthly.
Calculate amounts for when installments are made at the
beginning of each month and at the end of each month.
In the set up screen, specify “End” for Payment and “Fix2” for Display, and then
press J.
19 - 3 Compound Interest Calculations
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331
Perform the following key operation from the input screen.
f*bcw(Input n= 5 ×12.)
gw(I= 6.0%)
aw(PV = 0)
-cfaw
c
bcw(Monthly installments)
(Monthly compounding)
5(FV )
Specifying “Begin” for Payment in the set up screen changes to calculation of
installments at the beginning of each month.
5(FV )
uu
uu
uInstallment amount
Example Calculate the amount required for each installment to
accumulate a total of $10,000 in 5 years at an annual interest
rate of 6%, compounded semiannually.
In the set up screen, specify “End” for Payment, “Norm1” for Display, and then
press J.
Perform the following key operation from the input screen.
f*bcw(Input n= 5 ×12.)
gw(I= 6.0%)
aw(PV = 0)
c
baaaaw(FV = 10,000)
bcw(Monthly installments)
cw(Semiannual compounding)
4(PMT)
Compound Interest Calculations 19 - 3
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332
uu
uu
uNumber of installments
Example Calculate the number of monthly $84 installments required to
accumulate a total of $6,000 at an annual interest rate of 6%,
compounded annually.
In the set up screen, specify “End” for Payment and then press J.
Perform the following key operation from the input screen.
c
gw
aw(PV = 0)
-iew(PMT = –84)
gaaaw(FV = 6,000)
bcw(Monthly installments)
bw(Annual compounding)
1(n)
uu
uu
uInterest rate
Example Calculate the annual interest rate required to accumulate a
total of $10,000 in 10 years with $60 monthly installments.
In the set up screen, specify “End” for Payment and then press J.
Perform the following key operation from the input screen.
ba*bcw(Input n= 10 ×12.)
c
aw(PV = 0)
-gaw(PMT = –60)
baaaaw(FV = 10,000)
bcw(Monthly installments)
bw(Annual compounding)
2(I%)
uu
uu
uPrincipal plus interest with initial deposit
Example Calculate the principal plus interest after one year for an
installment savings account with an interest rate of 4.5%,
compounded monthly, opened with an initial deposit of $1,000,
with $500 installments added each month.
In the set up screen, specify “End” for Payment and then press J.
19 - 3 Compound Interest Calculations
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333
Perform the following key operation from the input screen.
b*bcw(Input n= 1 ×12.)
e.fw
-baaaw(PV = –1,000)
-faaw(PMT = –500)
c
bcw(Monthly installments)
(Monthly compounding)
5(FV)
uu
uu
uBorrowing power
Example Calculate how much can be borrowed on a 15-year loan at a
7.5% annual interest rate, compounded monthly, if a payment
of $450 per month can be made.
In the set up screen, specify “End” for Payment and then press J.
Perform the following key operation from the input screen.
bf*bcw(Input n= 15 ×12.)
h.fw
c
-efaw(PMT = –450)
aw(FV = 0)
bcw(Monthly installments)
(Monthly compounding)
3(PV)
uu
uu
uLoan installments
Example Calculate the size of the monthly installment for a 25-year
$300,000 home loan made at 6.2%, compounded semiannually.
In the set up screen, specify “End” for Payment and then press J.
Perform the following key operation from the input screen.
cf*bcw(Input n= 25 ×12.)
g.cw
daaaaaw(PV = 300,000)
c
aw(FV = 0)
bcw(Monthly installments)
cw(Semiannual compounding)
4(PMT)
Compound Interest Calculations 19 - 3
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334
uu
uu
uNumber of installments
Example Calculate the number of years it will take to repay a $60,000
loan borrowed at 5.5%, compounded monthly, with monthly
installments of $840.
In the set up screen, specify “End” for Payment and then press J.
Perform the following key operation from the input screen.
c
f.fw
gaaaaw(PV = 60,000)
-ieaw(PMT = –840)
aw(FV = 0)
bcw(Monthly installments)
(Monthly compounding)
1(n)
uu
uu
uEffective interest rate
Example Calculate (to two decimal places) the effective interest rate
compounded monthly, on a 25-year $65,000 loan repaid with
$460 monthly installments.
In the set up screen, specify “End” for Payment, “Fix2” for Display, and then press
J.
Perform the following key operation from the input screen.
cf*bcw(Input n= 25 ×12.)
c
gfaaaw(PV = 65,000)
-egaw(PMT = –460)
aw(FV = 0)
bcw(Monthly installments)
(Monthly compounding)
2(I%)
19 - 3 Compound Interest Calculations
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19-4 Investment Appraisal
This calculator uses the discounted cash flow (DCF) method to perform invest-
ment appraisal by totalling cash flow for a fixed period. This calculator can perform
the following four types of investment appraisal.
• Net present value (NPV)
• Net future 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
CF5CF6CF7
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.

336
uu
uu
uPBP
Initial value of Nwhen NPV >0.
Press 3(CASH) from the initial screen 1 to display the following input screen for
investment appraisal.
I% ................... interest rate
Csh ................. list for cash flow
•{NPV}/{IRR}/{PBP}/{NFV} ... {net present value}/{internal rate of return}/
{pay back period}/{net future value}
•{LIST} ... {specifies a list for cash flow}
Example An investment of $86,000 in machinery projects the annual
revenues shown in the table below (all revenues realized at the
end of the fiscal year). What is the net profit or loss of this
investment if the useful service life of the machine is six years,
the resale value after six years is $14,000, and the capital cost
is 11%?
Year Revenues
1 –5,000
2 42,000
3 31,000
4 24,000
5 23,000
6 12,000 + 14,000
On the Main Menu, select the LIST icon to enter the LIST Mode and perform the
following key operation.
e(List 2)
-igaaaw
-faaaw
ecaaaw
dbaaaw
ceaaaw
cdaaaw
bcaaa+beaaaw
Return to the Main Menu by pressing m. Select the TVM icon to enter the
Financial Mode, and then press 3(CASH).
19 - 4 Investment Appraisal

337
Investment Appraisal 19 - 4
Perform the following key operation from the input screen.
bbw(I% = 11)
6(List)2(List2)
1(NPV)
Now you can press 6(GRPH) to draw a cash flow graph.
6(GRPH)
Pressing !1 (TRCE) activates trace, which can be used to look up the
following values.
!6(G↔T)
4(NFV)
1(REPT)
3(PBP)
Example An investment of $10,000 in machinery projects the annual
revenues shown in the table below (all revenues realized at the
end of the fiscal year). What is the internal rate of return of this
investment if the useful service life of the machinery is five
years and the resale value after five years is $7,000?
Year Revenues
1 2,000
2 2,400
3 2,200
4 2,000
5 1,800 + 3,000

338
19 - 4 Investment Appraisal
On the Main Menu, select the LIST icon to enter the LIST Mode and perform the
following key operation.
ee(List 3)
-baaaaw
caaaw
ceaaw
ccaaw
caaaw
biaa+daaaw
Return to the Main Menu by pressing m. Select the TVM icon to enter the
Financial Mode, and then press 3(CASH).
Perform the following key operation from the input screen.
c
6(List)3(List 3)
2(IRR)
Now you can press 6to draw a cash flow graph.
6(GRPH)