Sharp El738 User Guide
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70 Linear regression calculation Example Key operation Result xym 1 1 Stat 1 000 252 > 5 JDATA SET=100 25 JDATA SET=200 12 2412 > 24 JDATA SET=300 21 21 2140 40 4021 > 40 > 3 J DATA SET=400 15 2515 > 25 JDATA SET=500 a = f a105a= b = f b183b= r = f r100r= sx = f 4854Sx= sy = f 51567Sy= x = 3 y´ = ?3 . ?6533y´ y = 46 x´ = ?46 . 9246246x´ DATA 2 4UBUJTUJDBM$BMDVMBUJPOTJOEE4UBUJTUJDBM$BMDVMBUJPOTJOEE1.1.
71 Quadratic regression calculation Example Key operation Result xym 1 2 Stat 2 000 12 4112 > 41 JDATA SET=100 8138 > 13 JDATA SET=200 525 > 2 JDATA SET=300 23 20023 > 200 JDATA SET=400 15 7115 > 71 JDATA SET=500 a = f a536a= b = f b-312b= c = f a050c= x = 10 y´ = ?10 . ?244910 y´ y = 22 x´ = ?22 . 9 @ @963≈¡= -343≈™= 963≈¡= 3 DATA 4UBUJTUJDBM$BMDVMBUJPOTJOEE4UBUJTUJDBM$BMDVMBUJPOTJOEE1.1.
72
Appendix
Financial Calculation Formulas
TVM solver
PMT, PV, FV, N
Error
I/Y
If PMT = 0 then
If N = 1 then
If PMT ≠ 0 or N ≠ 1 then fi nd i using the fol-
lowing equations:
+
Error
i≤ –1
Amortization calculations
Calculations
(for PV, PMT, and i, see the TVM solver)
END INT(1) = ROUND(–PV
× i)
BGN INT(1) = 0
PRN(1) = –INT(1) + ROUND(PMT)
BAL(1) = PRN(1) + PV
INT(m) = ROUND(–BAL(m – 1)
× i)
PRN(m) = –INT(m) + ROUND(PMT)
BAL(m) = PRN(m) + BAL(m – 1)
ROUND(NUM): If a display notation tab
setting has been chosen, NUM is rounded and
truncated to the specifi ed number of places
after the decimal point.
Results
Error
AMRT P1 > AMRT P2
Discounted cash fl ow
analysis
mm
CF
where i =
RATE(I/Y)
100, CFimax = the maxi-
mum data set number
IRR is obtained as i, which satisfi es NPV = 0
in the above equations.
QQFOEJYJOEEQQFOEJYJOEE1.1.
73 Bond calculations In its bond calculations, this calculator conforms to rules set up by the book titled Standard Securities Calculation Methods, by Jan Mayle, Securities Industry Association, 1993. Bond calculation is based on the following rules: 1. Whenever the redemption date happens to be the last day of a month, coupons are also paid on the last days of months. For example, if coupon payments are semi-annual and the redemp- tion date is September 30, coupon payments occur on March 31 and September 30. 2. If coupons are to be paid twice a year and the redemption date is set to August 29, 30, or 31, coupon payments for February occur on the 28th (29th for leap years). 3. The “Odd Coupon” is not supported. 4. All data stored or calculated for bonds are assumed to be posi- tive values. Negative values in any of the variables used by bond calculations will cause errors. The formulas used for bond calculations are shown using the follow- ing variable de nitions: TD: Total number of days in the coupon period that begins with the coupon date previous to the settlement date and ends with the rst coupon date after the settlement date. (On the 360-day calendar, TD is 180 for semi-annual coupon and 360 for annual coupon.) PD: The number of days preceding the settlement date in the cou- pon period described above. (see “Day and date calculations”) FD: The number of days following the settlement date in the coupon period described above (in TD). FD = TD – PD NP: The number of whole coupon periods between the settlement date and the redemption date (rounded up to the next highest whole number, if necessary). For one coupon period or less until redemption of bond: For more than one coupon period until redemption: where CPN = COUPON(PMT), RDV = REDEMPT(FV), N = CPN/Y(N), YIELD = YIELD(I/Y), PRICE = PRICE(PV). Yield is obtained as YIELD, which satisfi es the above equations. Error CPN < 0 or RDV < 0 or PRICE < 0 or M-D-Y 1 ≥ M-D-Y 2 or YIELD ≤ –100 QQFOEJYJOEEQQFOEJYJOEE1.1.
74
Depreciation calculations
ROUND(NUM): If a display notation tab
setting has been chosen, NUM is rounded and
truncated to the specifi ed number of places
after the decimal point.
In the following equations, M01 = START
MONTH, LIF = LIFE(N), CST = COST(PV),
SAL = SALVAGE(FV), and DB = DB(I/Y).
Straight-line method (SL)Calculations
If 1 < n < end_year then
Results
Sum-of-the-yearsʼ digits method (SYD)Calculations
Results
Declining balance method (DB)Calculations
Results
Error
CST < 0
SAL < 0
CST < SAL
LIF: when SL, LIF ≤ 0
when SYD or DB, LIF is not a positive
integer
I/Y < 0 (DB only)
Conversion between
APR and EFF
N, EFF
¬ APR
(( + 1) –1) N 100EFF
1001
N
Error
EFF ≤ –100
N, APR
¬ EFF
(( + 1) –1) 100APR
N
100N
Error
≤ –100APR
N
Day and date calculations
In day and date calculations, this calculator
conforms to rules set up in the book titled Stan-
dard Securities Calculation Methods, by Jan
Mayle, Securities Industry Association, 1993.
QQFOEJYJOEEQQFOEJYJOEE1.1.
75
30/360
1. Adjust D1 and D2 according to the fol-
lowing rules:
(1) If D2 and D1 are both the last day of
February, change D2 to 30.
(2) If D1 is the last day of February,
change D1 to 30.
(3) If D2 is 31 and D1 is 30 or 31, change
D2 to 30.
(4) If D1 is 31, change D1 to 30.
2. Calculate using the following formula:
DAYS = (Y2 – Y1)
× 360 + (M2 – M1)
×
30 + (D2 – D1)
Actual
Percent change/Compound
interest calculations
where NEW = NEW PRC(FV), OLD = OLD
PRC(PV), %CH = %(I/Y), PD = PERIODS(N)
Error
%CH ≤ –100
NEW
× OLD ≤ 0
Cost/Sell/Margin/Markup
calculations
where MAR = MARGIN, MU = MARK UP
Breakeven calculations
Statistical Calcula-
tion Formulas
Type Regression formula
Linear
y = a + bx
Quadraticy = a + bx + cx2
Exponentialy = a • ebx
Logarithmicy = a + b •
Inx
Powery = a • xb
Inverse 1
y = a + b
x
x = x
nΣ
sx = x2 – nx2
n – 1
Σ
x = x2 – nx2
nσΣ
x = x1 + x2 +
··· + xnΣ
x2 = x12 + x22 +
··· + xn2Σ
y = ynΣ
sy = y2 – ny2
n – 1
Σ
y = y2 – ny2
n
Σσ
y = y1 + y2 +
··· + ynΣ
y2 = y12 + y22 +
··· + yn2Σ
xy = x1y1 + x2y2 +
··· + xnynΣ
An error will occur in a statisti-
cal calculation if:
The absolute value of an
intermediate or calculation
result is equal to or greater
than 1
× 10
100.
The denominator is zero.
An attempt is made to nd
the square root of a negative
number.
No solution exists for a qua-
dratic regression calculation.
QQFOEJYJOEEQQFOEJYJOEE1.1.
76 Errors and Calculation Ranges Errors An error will occur if an operation exceeds the calculation rang- es, or if a mathematically illegal operation is attempted. When an error occurs, pressing g or y automatically moves the cursor back to the place in the equation where the error oc- curred. Edit the equation or press s to clear the equation. Note: If an error occurs during the automatic calculation of a listed nancial variable, pressing s, g, or y displays the rst variable in the function. Error codes and error types Syntax error (Error 1): An attempt was made to perform an invalid operation. Ex. 2 + - 5 = During the editing or insertion of cash ow or statistical data, a value was entered but . ? was pressed before J. Calculation error (Error 2): The absolute value of an intermediate or nal calculation result equals or exceeds 10 100. An attempt was made to divide by zero. The calculation ranges were exceeded while performing cal- culations. There was a nancial calculation error, such as: an error listed in “Financial Calculation Formulas” (see pages 72 – 75) occurred an attempt was made to nd I/Y when PV, PMT × N, and FV contain all negative or all positive values an attempt was made to nd IRR when the cash ow data contains all negative or all positive values an attempt was made to nd YIELD in a bond calculation when any of COUPON, REDEMPT, or PRICE contain negative values Depth error (Error 3): The available number of buffers was exceeded. (There are 10 buffers for numeric values and 24 buffers for calculation instructions). The number of entered cash ow and statistics data items combined exceeded 100. QQFOEJYJOEEQQFOEJYJOEE1.1.
77 Equation too long (Error 4): The equation exceeded its maximum input buffer (160 charac- ters). An equation must be shorter than 160 characters. No solution (Error 5): The iteration limit was exceeded while calculating one of the following values in an overly complex problem: I/Y (TVM solver) IRR (Discounted cash ow analysis) YIELD (Bond calculations) If you get an error while calculating IRR, enter an estimated value into RATE(I/Y) and calculate again. Display error (Error 6): An attempt was made to display “9.999 × 10 99” when the dis- play notation tab number was set to “2”. If this happens, press s and ~ 0 2 to set the display notation settings to “ oating point”. Then try again. Input value error (Error 7): An attempt was made to enter a nonexistent date. Ex. February 30th An attempt was made to enter an invalid numeric value into a nancial calculation. a negative value or 0 into P/Y or C/Y anything except an integer between 1 and 9,999 into AMRT P1 or AMRT P2 a non-integer into DAYS anything except 1 or 2 into CPN/Y anything except an integer between 1 and 999 as a cash ow frequency anything except a positive integer into YEAR anything except a value between 1 and 13 into START MONTH *1 *1 QQFOEJYJOEEQQFOEJYJOEE1.1.
78 Calculation ranges of functions Within the ranges speci ed, this calculator is accurate to within ±1 of the least signi cant digit of the mantissa. However, a calculation error increases in continuous calculations due to accumulation of each calculation error. (This is the same for nancial calculations, scienti c calculations [y x, x, ex, ln, n!, etc.], where continuous calculations are performed internally.) Additionally, a calculation error will accumulate and become larger in the vicinity of in ection points and singular points of functions. In nancial calculations, a calculation error increases if the interest is low or the number of payments is high. Press s if you’d like to cancel the calculation while the “calculating!” screen is displayed. Calculation ranges ±10 –99 to ±9.999999999 × 1099 and 0. If the absolute value of an entry or a nal or intermediate result of a calculation is less than 10 –99, the value is considered to be 0 in calculations and in the display. Function Calculation range sin x , cos x , tan xDEG: | x | < 1010 (tan x : | x | ≠ 90 (2n – 1))* π RAD: | x | < —×1010180 π (tan x : | x | ≠ — (2n – 1))* 2 10 GRAD: | x | < — × 10109 (tan x : | x | ≠ 100 (2n – 1))* sin –1 x , cos–1 x | x | ≤ 1 tan –1 x | x | < 10100 In x , log x 10 –99 ≤ x < 10100 yx y > 0: –10 100 < x log y < 100 y = 0: 0 < x < 10100 y < 0: x = n (0 < | x | < 1: 1 — x = 2n – 1, x ≠ 0),* –10 100 < x log | y | < 100 QQFOEJYJOEEQQFOEJYJOEE1.1.
79 Function Calculation range x y y > 0: –10 100 < 1 — x log y < 100 (x ≠ 0) y = 0: 0 < x < 10100 y < 0: x = 2n – 1 (0 < | x | < 1: 1 — x = n, x ≠ 0),* –10 100 < 1 — x log | y | < 100 ex –10 100 < x ≤ 230.2585092 10x –10 100 < x < 100 sinh x , cosh x , tanh x| x | ≤ 230.2585092 sinh –1 x | x | < 1050 cosh–1 x 1 ≤ x < 1050 tanh–1 x | x | < 1 x 2| x | < 1050 x 0 ≤ x < 10100 1/x | x | < 10 100 (x ≠ 0) n! 0 ≤ n ≤ 69* nPr0 ≤ r ≤ n ≤ 9,999,999,999* n! — < 10100(n – r)! nCr0 ≤ r ≤ n ≤ 9,999,999,999* 0 ≤ r ≤ 69 n! — < 10100(n – r)! * n, r: integer QQFOEJYJOEEQQFOEJYJOEE1.1.