{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier " 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "E rror" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 29 "Module 3 : Finite Mathematics" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 32 "302 : Sim ple & Compound Interest" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 17 "O B J E C T I V E " }}{PARA 0 "" 0 "" {TEXT -1 185 "We will learn to create financial fo rmulas and use these formulas to analyze and better understand how dif ferent conditions create different results using numeric and graphical methods." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 9 "S E T U P" }}{PARA 0 "" 0 "" {TEXT -1 252 "In this project we wi ll use the following command packages. Type and execute this line befo re begining the project below. If you re-enter the worksheet for this \+ project, be sure to re-execute this statement before jumping to any po int in the worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart; with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "_______________ ____________________________________________________________________" }}{PARA 4 "" 0 "" {TEXT -1 20 "A. Interest Formulae" }}{PARA 0 "" 0 " " {TEXT -1 83 "_______________________________________________________ ____________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 333 "There are a va riety of financial formulas you might encounter. We can create formula s in Maple to make financial computations. The format is this :\n \+ \011 \011(formula name as a continuous string of characters) := (list \+ of inputs) -> (forumula) ;\nUnlike Mathematics, we can use descriptive names for quantities rather than single letters." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 15 "SIMPLE INTEREST" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "Here is a formula for the amount at maturity of a simple interest loan." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 " simple_amt := (principal,interest_rate,years) -> principal + prin cipal*interest_rate*years;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+simpl e_amtGR6%%*principalG%.interest_rateG%&yearsG6\"6$%)operatorG%&arrowGF *,&9$\"\"\"*(F/F09%F09&F0F0F*F*F*" }}}{PARA 0 "" 0 "" {TEXT -1 11 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 393 " formula name : = list of inputs crude \+ arrow \011forumula ; \n not e that the \011\011\011\011\011\011 \+ \+ \011using the input values\n underscore \+ allows\n for a continuous string" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 7 "Problem" }{TEXT -1 97 " : Compu te how much you will have if you invest $2000 for 10 years at 9.5% usi ng simple interest." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 66 "Note that we express the interest rate, 9.5%, as a dec imal, .095." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 " simple_amt( 2000, .09, 10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'++Q!\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 17 "COMPOUND INTEREST" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "Here is a formula to compute th e maturity amount of a loan with compound interest." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 " compound _amt := (principal, interest_rate, years, compounds ) ->\n \+ principal*(1+interest_rate/compounds)^(years*compounds) ;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%-compound_amtGR6&%*principalG%.inter est_rateG%&yearsG%*compoundsG6\"6$%)operatorG%&arrowGF+*&9$\"\"\"),&F1 F1*&9%F19'!\"\"F1*&9&F1F6F1F1F+F+F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 201 "Interest rate is in decimal form, time period is in years, compounds is the number of times per year that co mpounds are computed (for example, 1 means annually, 4 mean quarterly, and 12 means monthly)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 7 "Problem" }{TEXT -1 97 " : Compute the amount you'll \+ have if you invest $6,000 at 5.25% for 3 years compounded quarterly." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 87 "Note th at there is no comma in 6000 and the interest rate is expressed in dec imal form." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 35 " compound_amt( 6000, .0525, 3, 4 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1 " 0 "" {MPLTEXT 1 0 60 " for k from 0 to 10 do compound_amt( 3000, .0725, k, 1) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%+I\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")+] " 0 "" {MPLTEXT 1 0 86 " for k from \+ 0 to 10 do \n simple_amt(3000, .11, k), compound_amt(3000, .11, k, 12 ) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"%+I\"\"!F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'+IL!\"#$\"+Bl:ZL!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'+gO!\"#$\"+$f&[MP!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'+!*R!\"#$\"+QfjmT!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\" '+?V!\"#$\"+;Uz[Y!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'+]Y!\"#$ \"+&HZn=&!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'+!)\\!\"#$\"+z;&p y&!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'+5`!\"#$\"+;5hck!\"'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'+Sc!\"#$\"+eDw.s!\"'" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$$\"'+qf!\"#$\"+3OPP!)!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"'++j!\"#$\"+j\"\\u'*)!\"'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 84 "We can also compare the results year by year of compounding annually versus monthly." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 " for k fr om 0 to 10 do \n compound_amt(3000, .0725, k, 1),compound_amt(3000 , .0725, k, 12) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"%+I\"\"!F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$\")+] " 0 "" {MPLTEXT 1 0 84 " plot( compound_amt( 1000, .0725, ceil(x), 1), x = 0. .20, labels = [years, amount]);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7\\[l7$$\"\"!F)$\"%+5F)7$$\"3gmmTN@Ki8! 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Exactly how much?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 " compound_amt( 1000, .04, 30, 12) - compoun d_amt( 1a);" }}{PARA 8 "" 1 "" {TEXT -1 31 "Error, missing operator or `;`\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "____ ______________________________________________________________________ _________" }}{PARA 4 "" 0 "" {TEXT -1 23 "D. The Financial Pacage" }} {PARA 0 "" 0 "" {TEXT -1 83 "_________________________________________ __________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 163 "Maple also has a financial package with built-in functions. For e xample, we can compute the effective rate of a loan using a Maple comm and in the finance package. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " with(finance): \+ \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " effectiverate( 0.105, 12 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*]M?5\"!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 253 "The effective interest rate of a compoun ded loan is the actual interest paid over a year. Sometimes this is kn own as APR (annual percentage rate) . This command computes the effect ive interest rate of a 10.5% loan compounded monthly (12 times per yea r)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?finance" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "0 0" 1 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }