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    Discrete Annual Compound Interest

    Interest Rate

     Year Cash Balance

    0 1,000.001

    2

    3

    4

    5

    !

    "

    #

    10

    $%&ord 'ni(ersit) *ress +2011 pp. "3-#3

    ote/ his discrete annual compound interest e%ample is &rom imon Bennina, Principles of F

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      inance with Excel, Second Edition

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    %cel uses standard *DA order o& operations &or

    *arentheses, %ponents, ultiplication and Di(ision, a

    *arentheses +-3%ponents - use caret 7 +&or e%a

    ultiplication - use asteris: ;

    Di(ision - use slash e >ant +-3+4=2 ? 1"

    ?-3;4=2

    Assume >e >ant +3

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      rithmetic

    nd Addition and u6traction

    ple, si% s8uared is 729 s8uare root o& si% is 7+.5

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    %ample

    natural lo lo to the 6ase e o& 1.5

    ln

    lo to the 6ase 2 lo to the 6ase 2 o& 1.5lo+num6er, 6ase

    pi 1 di(ided 6) the s8uare root o& pi

    pi+

    random num6er 6et>een 0 and 1

    ?rand+

    A B C D

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    11

    12

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    Ad@usted monthl) closin prices +&rom Yahoo nance

    Date  S&P 500 Index Duke Energy Stock  

    "

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    4

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    #

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    2

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    !

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    onthl) continuousl) compounded +lo returns

    S&P 500 Index Duke Energy Stock

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    1! months - 1!5 returns

    return data located ro>s 4 - 1!"

    Functions on one column at a time

    S&P 500 Index Duke Energy Stock

    a(erae monthl) return

    a(erae annual return

    standard de(iation o& monthl) returns

    annualied standard de(iation o& returns

    minimum

    ma%imum

    Functions on two columns at the same time (ordered pairs)

    S&P 500 Index - x axis Duke Energy Stock - y axis

    Description of best-t (regression) line - Duke on SP !""

    slope

    )-intercept

    correlation

    R-s8uared

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    14.5" )ears

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    Date S&P 500 Index Duke Energy Stock

    2

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    #

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    5

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    1

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    #

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    5

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    Discrete Annual Compound Interest 'se $EFR >hen G+% ? )

    >ant ) at a certain (alue,

    Interest Rate >ant ) at a ma%imum or

    10.00 i(en certain constraints o

     Year Cash Balance0 H1,000.00

    1 H1,100.00

    2 H1,210.00

    3 H1,331.00

    4 H1,44.10

    5 H1,10.51

    H1,!!1.5

    ! H1,#4".!2

    " H2,143.5#

    # H2,35!.#510 H2,5#3.!4

    use ol(er to calculate

    +1 hat discrete annual interest rate, at an initial 6alance o& H1,000

    +2 hat initial 6alance, at an interest rate o& 10, results in H5,000

    +3 Challene pro6lem

    uppose )ou >anted to :no>/ a&ter ho> man) )ears >ill H1000 at !

    Kint/ this re8uires re-structurin the &ormula so that the chanin nu

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    , or G+%1, %2, %3, etc ? ).

    r

    inimum,

    n (alues o& %.

    , results in H5,000 a&ter 10 )earsJ

     a&ter 10 )earsJ

    6e >orth H5,000J

      m6er o& )ears is located in one cell location

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    Discrete Annual Compound Interest

    Interest Rate

    !.00

     Year Cash Balance

    0 H1,000.00

    1 H1,0!0.00

    2 H1,144.#0

    3 H1,225.04

    4 H1,310."0

    5 H1,402.55 H1,500.!3

    ! H1,05.!"

    " H1,!1".1#

    # H1,"3".4

    10 H1,#!.15

    A&ter ho> man) )ears >ill H1000 at ! 6e >orth H5,0

    num6er o& )ears 10

    restated &ormula

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    0J

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    Cop)riht Daniel

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      er< Attri6ution 4.0 Inter

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    ational +CC BY 4.0