University of Jordan
College of Science
Department of Mathematics
Database Management
In
Excel (Windows XP)
Dr. Mohammad Al-Raqab
Fall 2005-2006
1
I. General Introduction-Excel
The MS Excel is an electronic spreadsheet. An electronic spreadsheet is a tool to organize
information in tables. The financial analysts, biologists, engineers, marketing specialists and
managers use the electronic spreadsheets. Excel files are called workbooks, which contain
worksheets. A worksheet consists of rows and columns. The rows are numbered and letters
identify the columns. The intersection of a row and column is called a cell, which is a box that
can store a number, word or formula. The elements of the Excel window are
(1) Title Bar: Name of the book (document).
(2) Menu Bar: Provides access to the commands on the menus.
(3) Tools Bar: Summary of assorted commands.
(4) Vertical Scroll Bar: Move backword and forward in your document.
(5) Formula Bar: This allows you to see the contents of the active cell.
(6) Status Bar: Displaying information about the document as well as the information
about the position of the insertion pointer.
If you click the New icon (the first icon on the Toolbar) you will see the following window. Note
that the cell in row 1 column A is active, which means that you can type in a number, word or
formula. You can designate any cell as active by moving the mouse pointer (which now
appears as a large plus sign) and clicking. Alternatively, you can use any of the four Up, Down,
Left, or Right arrow keys.
At the bottom of the screen you will see the word Ready. As you begin to type something into
the active cell, the word changes to Enter. Above this word you will find the following tabs:
Sheet1, Sheet2, and Sheet3, the three worksheets that comprise this worksheet. You can
operate on any of these as well as other sheets that may be created.
2
Editing Data:
Each statistical technique requires that the data be in some specific format. If the data are
not in that form, it will be necessary to edit the data. As a first step, you must highlight the data
you wish to edit. To do so, place the mouse pointer over the first cell of the range, and hold the
left button down as you move the mouse over the range. Alternatively, you can activate the first
cell of the range, hold down the Shift key, and use the Up, Down, Left, or Right arrow keys to
highlight the range.
To delete the range, hit the delete key.
To move up the range, place the mouse pointer at the top right corner of the range,
depress the left mouse button, and move the mouse until the range is where you wish it to be.
Release the button. Alternatively, click Edit and Cut. Activate the cell where the top of the
range will be located, and click Edit and Paste.
You can also use similar commands to copy a range of data. Instead of Cut, click Copy.
II. Performing Statistical Procedures:
There are several ways to conduct a statistical analysis. These are Data Analysis, Data
Analysis Plus, Stats-summary.xls, and the Toolbar function fx.
Data Analysis/Analysis ToolPak
The Analysis ToolPak is a group of statistical functions that comes with excel. The Analysis
ToolPak can be accessed through the Menu bar. Click Tools and Data Analysis …(Note that
Analysis ToolPak is not the same as Analysis ToolPak-VBA.) If Data Analysis … does not
appear, click Add-Ins … and select Analysis ToolPak. If Analysis ToolPak is not shown, you
will need to install if from the original Excel or MS Office diskettes or CD-ROM. Run the setup
program, and follow instructions.
There are 20 menu items in Data Analysis … Click the one you wish to use, and follow the
instructions described in this book. For example, the first technique in the menu: Anova: Single
Factor.
Data Analysis Plus:
Data Analysis Plus is another collection of macros created to augment Excel's list of statistical
procedures: Data Analysis Plus (STATS.XLS) is supplied and accompanied in some applied
statistics books. The Stats.xls - must be stored in the XLStart folder on your hard drive. To
install it,
-
You must find the XLStart folder. Under Windows, choose the Start Button, Find, and
then type “XLStart” into the dialog box and click Find. Be sure to search all hard drives.
The find dialog box will display the path to where the XLStart folder is. Make sure Excel
is not running – Quit Excel if it is running.
-
Navigate to the XLStart folder on your hard drive. Open the Data Analysis Plus3.0
folder on the CD, select the Stats.xls file and drag it to the XLStart folder on the hard
drive. Restart Excel.
If you have multiple copies of Excel on your machine, make sure you install the Stats.xls file in
the folder of the copy of Excel you want to use.
3
-
If the above steps have been done correctly, the Data Anaysis Plus will become a
menu in the Tools heading in the Menu Bar. Note that It contains 24 menu items.
Excel with macros tool has a potential capabilities. It includes graphical representation,
descriptive and inferential statistics (frequency tables, graphical representation, statistical
measures, comparing between means, goodness-of-fit-test, equality of variances, regression
and correlation, nonparametric approaches). It can export and import the data easily.
Comparing with SAS or SPSS, it has less powerful in dealing with huge number of data or
complicated situations.
III- Mathematical Formula:
Formulas are equations that perform calculations on values in your worksheet. A formula starts
with an equal sign (=). For example, the following formula multiplies 2 by 3 and then adds 5 to
the result.
=5+2*3
A formula can also contain any or all of the following:
- The PI() function returns the value of pi: 3.142...
- References (or names): A2 returns the value in cell A2. A reference identifies a cell
or a range of cells on a worksheet and tells Microsoft Excel
where to look for the values or data you want to use in a
formula.
- Constants: Numbers or text values entered directly into a formula, such as 2.
- Operators: The ^ (caret) operator raises a number to a power, and the * (asterisk)
operator multiplies.
Comparison operator
= (equal sign)
> (greater than sign)
< (less than sign)
>= (greater than or equal to sign
<= (less than or equal to sign)
<> (not equal to sign)
Meaning (Example)
Equal to (A1=B1)
Greater than (A1>B1)
Less than (A1<B1)
Greater than or equal to (A1>=B1)
Less than or equal to (A1<=B1)
Not equal to (A1<>B1)
Example 1: Consider the following data set (stored in letterGrade.xls):
Name
Ahmad
Ali
Muna
Khalid
Raed
Fatima
Alaa
City
Amman
Amman
Salt
Irbid
Zarqa
Amman
Aqaba
Sex
M
M
F
M
M
F
M
Grade
60
77
92
85
88
34
69
(a) Find the sum of grades of the students
4
(b) Find the average of the grades of the students.
(c) Change the grades to the letter grades (A: >=90, B:80-89,C:70-79, D:60-69,
F:<60).
(a) To find the sum of grades
1- First enter the data in the worksheet as follows:
2- Position the cursor in the cell you wish to include the result in.
3- Write = Sum(D2:D8)
4- Enter. The result = 505.
You can use the function fx which includes some basic functions (Sum, average,
Max, Min.,…). In this case,
- Choose the sum from the dialog box (Insert function)
-
In the Box (Function Arguments), write the range of your data A2:D8.
(b) Write =Average(D2:D8). The result= 72.14286.
(c) IF(logical_test,value_if_true,value_if_false): Logical_test is any value or
expression that can be evaluated to TRUE or FALSE. For example, A10=100 is a
logical expression; if the value in cell A10 is equal to 100, the expression evaluates to
TRUE. Otherwise, the expression evaluates to FALSE.
=IF(A2<=100,"Within
budget","Over budget")
If the number above is less than or equal to
100, then the formula displays "Within
budget". Otherwise, the function displays
"Over budget" (Within budget)
=IF(A2=100,SUM(B5:B15),"") If the number above is 100, then the range
B5:B15 is calculated. Otherwise, empty text
("") is returned ()
In our example, I can apply the if statement to cell D2 (which contains the number
60).
- Choose any empty cell.
- Write the following command:
=IF(D2>=90,"A",IF(D2>=80,"B",IF(D2>=70,"C",IF(D2>=60,"D","F"))))
5
-
Enter. You will get D.
Dragging the fill handle of the cell D2 to all cells in the column D. Then
we will have
D
C
A
B
B
F
D
IV. Graphical Representation:
1- Frequency Distribution and Histograms:
Example 2: The following data stored in Xm04-2.xls represent the length time
(in minutes) spent to finish a certain task. Develop a frequency distribution and
histogram to describe the data.
The classes are defined below:
Classes
More than 10 but less than or equal to 25 minutes
More than 25 but less than or equal to 40 minutes
More than 40 but less than or equal to 55 minutes
More than 55 but less than or equal to 70 minutes
More than 70 but less than or equal to 85 minutes
More than 85 but less than or equal to 100 minutes
More than 100 but less than or equal to 115 minutes
More than 115 but less than or equal to 130 minutes
More than 130 but less than or equal to 145 minutes
More than 145 but less than or equal to 160 minutes
Consider the following command code:
Import Xm04-2.xls /B1=Limits, B2=upper limit of the first class,
B3=upper limit of the second class, and so on to complete the listing of upper
limites//Tools/Data Analysis/Histogram: Input Range: A1:A401/Bin Range:
B1:B11(if the name of variable is included, click label/Chart Output/OK/
Click (with left button) Format Data Series/Options: Gap Width: change 150
to 0/OK/To remove More, Click Clear(with right button).
The Frequency Distribution and the histogram are given by
Limits
25
40
55
70
85
100
115
130
145
160
Frequency
3
106
150
83
30
16
8
2
1
1
6
2- Bar and Pie Charts for Normal Data:
Example 3 (Xm04-3.xls): The data represent the area of employments of graduates
as follows:
1=Accounting, 2=Finance, 3=General Management, 4=Market/Sales
Consider the following command code:
B1=Bins, B2=1, B3=2,B4=3,B5=4,B6=5
Tools/Data Analysis/Histogram: Input Range: A1:A254/Input Range: B1:B6
(if the name of variable is included, click label/Chart/Choose Column for Bar
Chart and Pie for Pie Chart
Frequency
150
100
Frequency
50
0
2
3
4
More
Area
Frequency
11%
2
25%
50%
3
4
More
14%
Pie Chart of Area
7
3- Line Charts for Time Series Data
Example 4 (Xm04-4.xls): Data on the weekly revenues of a restaurant for the 10
weeks
Week
Revenue
1
4854
2
5337
3
5205
4
5402
5
6001
6
5883
7
6309
8
5969
9
6040
10
6432
Command Code:
Highlight the Data Column/Chart Wizard/Choose Line/Finish
7000
6000
5000
4000
3000
2000
1000
0
Series1
1
2
3
4
5
6
7
8
9 10
4-Scatter Diagrams (Two Continuous Variables)
Example 5 (Xm04-5.xls): The data here are given on 2 variables: # of years he/she
completed the degree and his/her income for the previous 12 months.
Highlight the Data Column/Chart Wizard/Choose XY (Scatter)/Chart Subtype/Data Range, Input Range A1:B151/Next …Finish/Title:Scatter Diagram,XAxis=Education, Y-Axis=Income/Gridlines: remove check mark/Finish. To draw line:
Chart and choose Trendline/OK/
Chart Title
120
100
80
60
40
20
0
Income
0
10
20
30
V- Descriptive Statistics:
Example 6 (Xm04-2.xls):
Command Code:
Tools/Data Analysis/Descriptive Statistics/Input Range:A1:A401/Summary
Statistics/OK/
8
Times
Mean
Standard
Error
Median
Mode
Standard
Deviation
Sample
Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
52.7
0.981987
48
41
19.63974
385.7193
2.706016
1.382361
128
23
151
21080
400
VI-Computations of Normal Probabilites:
Click fx /Function Category:Statistical/ Function Name: NormDistribution/Ok/
Type the value of X=…, Mean=…,Std.=…, True(cumulative)/OK/
Short Command Code: =NORMDIST(20,10,5,TRUE)
VII- Simple Random Sample:
Example 8: (Generate 50 numbers between 1 and 1000)
Tools/Data Analysis/Random Number Generation/Number of Variables=1, No. of
Random Number=50/Uniform Distribution, parameters 0 and 1/OK/Col.
B=1000*Col.A/Active Cell C1/Click fx , Math.&Trig.Round up/Next/Specify the first
number to be rounded B1/Type # of digits (decimal places): 0/Finish/Complete Col. C.
9
VIII-Estimation and Testing Using t-distribution:
Example 9 (Xm04-9): A sample of 240 households was drawn and the weekly weight
of newspapers discarded for recycling for each household was recorded.
(1) Estimate the mean weight of newspapers by 95% confidence Interval.
(2) Do these data provide sufficient evidence to conclude that recycling newspapers is a
viable project (mean weight is more than 2 pounds)?
Command Code:
Click fx/Choose Statistical,T INV/ Insert probability=P(|T|>t)=0.05 and df=239
You will get t=1.9699 (cut-of-point for 95% C.I.)
Tools/Data Analysis Plus/t-estimates and test/Input Range A2:A241, Label, Hypothesized
Mean/OK/
(a) The 95% C.I. for the mean is 2.0904 ± 1.9699(0.0268)
(b) Test statistic=3.3769, p-value=0.0004, Reject the null hypothesis and the mean weight
is more 2 pounds.
t-Test and Estimate: Mean
Column 1
2.0904
0.4148
2
239
3.3769
0.0004
1.6513
0.0008
1.9699
0.0268
0.052794
2.037622
2.143211
Mean
Standard Deviation
Hypothesized Mean
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Standard Error
Bound
LCL
UCL
Similarly you can use z-test since the sample size is large.
OR: You can apply Stats-Summary to determine 95% C.I. for the mean.
t-Test of a Mean
8110
Sample mean
Sample standard
deviation
Sample size
270.5
16
Hypothesized mean
8200
t Stat
P(T<=t) one-tail
P(T<=t) two-tail
-1.33
0.1016
0.2031
10
You have to change the sample mean=2.0904, standard deviation=0.4148 and sample
size=240 and Hypothesized mean=2, to get the following 95% C.I. for the mean:
t-Test of a Mean
Sample mean
Sample standard
deviation
Sample size
2.0904
0.4148
240
Hypothesized mean
2
t Stat
P(T<=t) one-tail
P(T<=t) two-tail
3.38
0.0004
0.0009
Normality Test:
Command Code: Tools/Data Analysis Plus/ChiSquare Test of Normality
Chi-Squared Test of Normality
Mean
Standard
deviation
Observations
Intervals
(z <= -2)
(-2 < z <= -1)
(-1 < z <= 0)
(0 < z <= 1)
(1 < z <= 2)
(z > 2)
chi-squared Stat
df
p-value
chi-squared
Critical
Column 1
2.092148136
0.4146
240
Probability
0.02275
0.135905
0.341345
0.341345
0.135905
0.02275
Expected
5.46
32.6172
81.9228
81.9228
32.6172
5.46
Observed
7
31
75
91
32
4
2.5074
3
0.474
7.8147
Using the p-value=0.474, we conclude that the normality follows.
IX- Inferences about Proportions:
Example 10 (Xm04-10.xls): Data on Election and the responses were 1= Democrat,
2=Republican. The responses of a sample of 926 voters.
(a) Obtain 95% C.I. for p=proportion of democrat.
Command Code: Tools/Data Analysis Plus/z-test and estimate proportion/Input Range
A2:A241/Success=1/Ok/
95% C.I. for p is (0.502, 0.567).
11
z-Test and Estimate: Proportion
Column 1
Sample
Proportion
Observations
Hypothesized Proportion
z Stat
P(Z<=z) one-tail
z Critical one-tail
P(Z<=z) two-tail
z Critical two-tail
0.5346
926
0.5
2.1032
0.0177
1.6449
0.0354
1.96
Standard Error
Bound
LCL
UCL
0.0164
0.032143
0.502414
0.566701
(b) Can you conclude that the proportion of democrat is different from 50%? Use α =0.05.
H0: p=0.5, vs. H1: p ≠ 0.5
Z-test = 2.1032, critical z=1.96 so we reject H0.
X- Comparing between Means:
Example 11 (Xm04-11.xls):
The assembly times for 25 workers in minutes were
recorded using two methods. We would like to know whether the assembly times of the two
methods differ.
Assuming Not Equal Variances:
H0: μ A = μ B vs. H1: μ A ≠ μ B
Tools/Data Analysis/ t-test: Two-Sample Assuming Unequal Variances/Input: Variable
1 Range A2:A26, Variable 2 Range: B2:B26/Hypothesized Mean Difference:0/Click
Label if applicable/specify α /OK/
t-Test: Two-Sample Assuming Unequal Variances
Variable 1
Variable 2
Mean
6.288
6.016
Variance
0.847767
1.303067
Observations
25
25
Hypothesized
Mean Difference
0
df
46
t Stat
0.927333
P(T<=t) one-tail
0.179297
t Critical one-tail
1.67866
P(T<=t) two-tail
0.358594
t Critical two-tail
2.012896
12
Assuming Equal Variances:
H0: μ A = μ B vs. H1: μ A ≠ μ B
Tools/Data Analysis/ t-test: Two-Sample Assuming Equal Variances/Input: Variable 1
Range A2:A26, Variable 2 Range: B2:B26/Hypothesized Mean Difference:0/Click
Label if applicable/specify α /OK/
t-Test: Two-Sample Assuming Equal Variances
Variable 1
Variable 2
Mean
6.288
6.016
Variance
0.847767
1.303067
Observations
25
25
Pooled Variance
1.075417
Hypothesized Mean
Difference
0
df
48
t Stat
0.927333
P(T<=t) one-tail
0.179197
t Critical one-tail
1.677224
P(T<=t) two-tail
0.358393
t Critical two-tail
2.010635
The p-value is 0.3584. There is no significance difference between method A and
method B.
Using Worksheet Stats-Summary.xls
(t-Estimate of the Difference Between Two Means (Equal-Variances))
t-Estimate of the Difference Between Two
Means (Equal-Variances)
Sample 1
Sample mean
Sample standard deviation
Sample size
6.2880
0.921
25
Sample 2
Sample mean
Sample standard deviation
Sample size
Confidence level
Pooled Variance estimate
6.0160
1.1420
25
0.95
1.0762
Difference between means
Bound
Lower confidence limit
Upper confidence limit
0.2720
0.5900
-0.3180
0.8620
13
Financial Mathematics Functions
1. Present Value:
Returns the present value of an investment. The present value is the total amount that
a series of future payments is worth now. For example, when you borrow money, the
loan amount is the present value to the lender.
Syntax
PV(rate,nper,pmt,fv,type)
Rate: is the interest rate per period. For example, if you obtain an automobile loan
at a 10 percent annual interest rate and make monthly payments, your interest rate per
month is 10%/12, or 0.83%. You would enter 10%/12, or 0.83%, or 0.0083, into the
formula as the rate.
Nper:
is the total number of payment periods in an annuity. For example, if you
get a four-year car loan and make monthly payments, your loan has 4*12 (or 48)
periods. You would enter 48 into the formula for nper.
Pmt:
is the payment made each period and cannot change over the life of the
annuity. Typically, pmt includes principal and interest but no other fees or taxes. For
example, the monthly payments on a $10,000, four-year car loan at 12 percent are
$263.33. You would enter -263.33 into the formula as the pmt. If pmt is omitted, you
must include the fv argument.
Fv is the future value, or a cash balance you want to attain after the last payment is
made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is
0). For example, if you want to save $50,000 to pay for a special project in 18 years,
then $50,000 is the future value. You could then make a conservative guess at an
interest rate and determine how much you must save each month. If fv is omitted, you
must include the pmt argument.
Type: is the number 0 or 1 and indicates when payments are due.
Set type equal to
If payments are due
0 or omitted
At the end of the period
1
At the beginning of the period
Remarks
•
Make sure that you are consistent about the units you use for specifying rate and nper.
If you make monthly payments on a four-year loan at 12 percent annual interest, use
12%/12 for rate and 4*12 for nper. If you make annual payments on the same loan,
use 12% for rate and 4 for nper.
•
The following functions apply to annuities:
14
CUMIPMT
CUMPRINC
FV
FVSCHEDULE
IPMT
PMT
PPMT
PV
RATE
XIRR
XNPV
An annuity is a series of constant cash payments made over a continuous period. For
example, a car loan or a mortgage is an annuity. For more information, see the description
for each annuity function.
•
•
In annuity functions, cash you pay out, such as a deposit to savings, is represented by
a negative number; cash you receive, such as a dividend check, is represented by a
positive number. For example, a $1,000 deposit to the bank would be represented by
the argument -1000 if you are the depositor and by the argument 1000 if you are the
bank.
Microsoft Excel solves for one financial argument in terms of the others. If rate is not 0,
then:
nper
Pv*(1+rate)
(1 + rate) nper − 1
+ pmt*(1+rate*type)*(
) + fv
rate
If rate is 0, then:
(pmt * nper) + pv + fv = 0
If rate is 0, then:
(pmt * nper) + pv + fv = 0
Example: The example may be easier to understand if you copy it to a blank
worksheet.
1.
2.
3.
4.
5.
Create a blank workbook or worksheet.
Select the example in the Help topic. Do not select the row or column headers.
Press CTRL+C.
In the worksheet, select cell A1, and press CTRL+V.
To switch between viewing the results and viewing the formulas that return the results,
press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and
then click Formula Auditing Mode.
15
A
Data
B
Description
Money paid out of an insurance annuity at the end of every
500
month
8%
Interest rate earned on the money paid out
20
Years the money will be paid out
Formula
Description (Result)
=PV(A3/12, 12*A4, A2, , 0) Present value of an annuity with the terms above (-59,777.15).
The result is negative because it represents money that you would pay, an outgoing
cash flow. If you are asked to pay (60,000) for the annuity, you would determine this
would not be a good investment because the present value of the annuity (59,777.15)
is less than what you are asked to pay.
Note: The interest rate is divided by 12 to get a monthly rate. The years the money is
paid out is multiplied by 12 to get the number of payments.
2. Net Present Value NPV:
Calculates the net present value of an investment by using a discount rate and a series
of future payments (negative values) and income (positive values).
Syntax
NPV(rate,value1,value2, ...)
Rate: is the rate of discount over the length of one period.
Value1, value2, ... are 1 to 29 arguments representing the payments and income.
•
•
•
•
Value1, value2, ... must be equally spaced in time and occur at the end of each period.
NPV uses the order of value1, value2, ... to interpret the order of cash flows. Be sure to
enter your payment and income values in the correct sequence.
Arguments that are numbers, empty cells, logical values, or text representations of
numbers are counted; arguments that are error values or text that cannot be translated
into numbers are ignored.
If an argument is an array or reference, only numbers in that array or reference are
counted. Empty cells, logical values, text, or error values in the array or reference are
ignored.
Remarks:
•
The NPV investment begins one period before the date of the value1 cash flow and
ends with the last cash flow in the list. The NPV calculation is based on future cash
flows. If your first cash flow occurs at the beginning of the first period, the first value
must be added to the NPV result, not included in the values arguments. For more
information, see the examples below.
16
•
If n is the number of cash flows in the list of values, the formula for NPV is:
n
NPV =
values j
∑ (1 + rate)
j =1
•
•
j
.
NPV is similar to the PV function (present value). The primary difference between PV
and NPV is that PV allows cash flows to begin either at the end or at the beginning of
the period. Unlike the variable NPV cash flow values, PV cash flows must be constant
throughout the investment. For information about annuities and financial functions, see
PV.
NPV is also related to the IRR function (internal rate of return). IRR is the rate for which
NPV equals zero: NPV(IRR(...), ...) = 0.
Example 1:
The example may be easier to understand if you copy it to a blank worksheet.
1.
2.
3.
4.
5.
Create a blank workbook or worksheet.
Select the example in the Help topic. Do not select the row or column headers.
Press CTRL+C.
In the worksheet, select cell A1, and press CTRL+V.
To switch between viewing the results and viewing the formulas that return the results,
press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and
then click Formula Auditing Mode.
A
B
Data
Description
10%
Annual discount rate
-10,000
Initial cost of investment one year from today
3,000
Return from first year
4,200
Return from second year
6,800
Return from third year
Formula
Description (Result)
=NPV(A2, A3, A4, A5, A6) Net present value of this investment (1,188.44)
In the preceding example, you include the initial $10,000 cost as one of the values,
because the payment occurs at the end of the first period.
Example 2:
The example may be easier to understand if you copy it to a blank worksheet.
1. Create a blank workbook or worksheet.
2. Select the example in the Help topic. Do not select the row or column headers.
3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results,
press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and
then click Formula Auditing Mode.
17
A
Data
B
Description
Annual discount rate. This might represent the rate of inflation or
8%
the interest rate of a competing investment.
-40,000
Initial cost of investment
8,000
Return from first year
9,200
Return from second year
10,000
Return from third year
12,000
Return from fourth year
14,500
Return from fifth year
Formula
Description (Result)
=NPV(A2, A4:A8)+A3
Net present value of this investment (1,922.06)
Net present value of this investment, with a loss in the sixth year
=NPV(A2, A4:A8, -9000)+A3
of 9000 (-3,749.47)
In the preceding example, you don't include the initial $40,000 cost as one of the
values, because the payment occurs at the beginning of the first period.
3. Cumulative Principal CUMPRINC :
Returns the cumulative principal paid on a loan between start_period and end_period.
If this function is not available, and returns the #NAME? error, install and load the
Analysis ToolPak add-in.
1. On the Tools menu, click Add-Ins.
2. In the Add-Ins available list, select the Analysis ToolPak box, and then click OK.
3. If necessary, follow the instructions in the setup program.
Syntax
CUMPRINC(rate,nper,pv,start_period,end_period,type)
Rate: is the interest rate.
Nper: is the total number of payment periods.
Pv: is the present value.
Start_period: is the first period in the calculation. Payment periods are numbered
beginning with 1.
End_period: is the last period in the calculation.
Type: is the timing of the payment.
Type
Timing
0 (zero)
Payment at the end of the period
1
Payment at the beginning of the period
18
Remarks:
•
•
•
•
•
Make sure that you are consistent about the units you use for specifying rate and nper.
If you make monthly payments on a four-year loan at an annual interest rate of 12
percent, use 12%/12 for rate and 4*12 for nper. If you make annual payments on the
same loan, use 12% for rate and 4 for nper.
Nper, start_period, end_period, and type are truncated to integers.
If rate ≤ 0, nper ≤ 0, or pv ≤ 0, CUMPRINC returns the #NUM! error value.
If start_period < 1, end_period < 1, or start_period > end_period, CUMPRINC returns
the #NUM! error value.
If type is any number other than 0 or 1, CUMPRINC returns the #NUM! error value.
Example:
The example may be easier to understand if you copy it to a blank worksheet.
1.
2.
3.
4.
5.
Create a blank workbook or worksheet.
Select the example in the Help topic. Do not select the row or column headers.
Press CTRL+C.
In the worksheet, select cell A1, and press CTRL+V.
To switch between viewing the results and viewing the formulas that return the results,
press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and
then click Formula Auditing Mode.
A
Data
B
Description
9.00%
Interest rate per annum
30
Term in years
125,000
Present value
Formula
Description (Result)
The total principal paid in the second year of
=CUMPRINC(A2/12,A3*12,A4,13,24,0)
payments, periods 13 through 24 (-934.1071)
The principal paid in a single payment in the first
=CUMPRINC(A2/12,A3*12,A4,1,1,0)
month (-68.27827)
Note The interest rate is divided by 12 to get a monthly rate. The years the money is
paid out is multiplied by 12 to get the number of payments.
4. Effect:
Returns the effective annual interest rate, given the nominal annual interest rate and
the number of compounding periods per year. If this function is not available, and
returns the #NAME? error, install and load the Analysis ToolPak add-in.
1. On the Tools menu, click Add-Ins.
2. In the Add-Ins available list, select the Analysis ToolPak box, and then click OK.
3. If necessary, follow the instructions in the setup program.
19
Syntax
EFFECT(nominal_rate,npery)
Nominal_rate: is the nominal interest rate.
Npery: is the number of compounding periods per year.
Remarks:
•
•
•
•
Npery is truncated to an integer.
If either argument is nonnumeric, EFFECT returns the #VALUE! error value.
If nominal_rate ≤ 0 or if npery < 1, EFFECT returns the #NUM! error value.
EFFECT is calculated as follows:
Effect = (1+
No min al _ rate Nper
) -1
Nper
Example:
The example may be easier to understand if you copy it to a blank worksheet.
1.
2.
3.
4.
5.
Create a blank workbook or worksheet.
Select the example in the Help topic. Do not select the row or column headers.
Press CTRL+C.
In the worksheet, select cell A1, and press CTRL+V.
To switch between viewing the results and viewing the formulas that return the results,
press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and
then click Formula Auditing Mode.
A
Data
B
Description
5.25%
Nominal interest rate
4
Number of compounding periods per year
Formula
Description (Result)
=EFFECT(A2,A3) Effective interest rate with the terms above (0.053543 or 5.3543 percent)
20