Exercise 11. <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> </head> <body> </body> </html>

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1 Exercise 11 The purpose of this exercise is to demonstrate the similarity between different program languages. In this exercise, we will use Javascript to make the same Time Value of Money Solver as in the problem 2) of Exercise 10. Javascript is a program language used by web browsers. With the power of JavaScript, web programmers can transform web pages from simple documents into interactive applications. We need to make a html (HyperText Markup Language) file. HTML is the language used for web pages. Please open Notepad on a Windows computer or TextEdit on a Mac computer, and copy the following code and paste it in your file. <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> </head> <body> </body> </html> Save it as Ex11-Yourlastname.html (for example, Ex11-Wang.html). In Notepad, you need to change the Save as type: to All Files (*.*). On Mac s TextEdit, you need to set the Preferences... Format to Plain text. To display it, just double click the file. It is an empty web page because there is nothing between the <body> </body> tag. Note: Do not use Internet Explorer. This Exercise can be properly displayed in any web browser except Internet Explorer. To choose your browser, right click the file, click Open with, then choose either Google chrome or Firefox. Next, download the picture file blueback.jpg and save it in the same folder as your html file, and add more lines to the html file: <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> </head> <body background=blueback.jpg > <FONT face=arial color=#000080> <h2> Time Value of Money Solver </h2>

2 <p> Please type in the known quantities, leave the quantity to be solved empty, and click Solve button to solve it. Keep in mind that the cash flow in different directions have opposite signs. </p> </body> </html> Save it, and refresh your browser. You then can see the change. The picture blueback.jpg becomes the background of the web page, <FONT face=arial color=#000080> specify the font face and color of the page, <h2> </h2> tag defines a 2nd level heading, and <p> </p> tag defines a paragraph of text. Just like the maplet in problem 2 of Exercise 10, we will make our TVM solver using tables. We first make some small tables, and then use a big table to group small tables together and add some style. The first 2 lines are two tables defined by following red code: <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> </head> <body background=blueback.jpg> <FONT face=arial color=#000080> <h2> Time Value of Money Solver </h2> <td>number of Payments: <td><input style="width:120px"> <td>interest Rate per Year: <td><input style="width:120px"> <td>% <td>present Value: $ <td><input style="width:120px"> <td style="width:5px"> <td>payment: <td style="width:5px"> $ <td><input style="width:120px">

3 <td>future Value: </body> </html> $ <td><input style="width:120px"> Each tag defines a table where each table row is defined by the <tr> tag and each table data/cell is defined by the <td> tag. style option can be used to define styles of the table row or table cell. The <input> tag here is similar to the TextField in a maplet, it defines an input text field (other objects are also defined by <input> tag with different styles). Also an empty table cell with specified width is add to define a white space. Two sliders are contained in the third table. Unlike the Maple, a slider is not a predefined object in HTML. We need to define it first before using it. Add the following red code to your file: <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> <style>.slidecontainer {width: 100%;.slider { -webkit-appearance: width: 100%; height: 5px; border-radius: background: outline: none; opacity: 0.7; 5px; #d3d3d3; -webkit-transition: transition: none;.2s; opacity.2s;.slider:hover { opacity: 1;.slider::-webkit-slider-thumb {

4 -webkit-appearance: none; appearance: none; width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer;.slider::-moz-range-thumb { width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer; </style> </head> <body background=blueback.jpg> <FONT face=arial color=#000080> <h2> Time Value of Money Solver </h2> <td>number of Payments: <td><input style="width:120px"> <td>interest Rate per Year: <td><input style="width:120px"> <td>% <td>present Value: $ <td><input style="width:120px"> <td style="width:5px"> <td>payment: $ <td><input style="width:120px"> <td style="width:5px">

5 <td>future Value: $ <td><input style="width:120px"> <tr> <td>number of Payments per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider"> </div> <tr style="height:10px"> <tr> <td>number of Compounding per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider"> </div> </body> </html>

6 The slider is defined in the <style> </style> tag inside the <head> </head> tag. The new table has 3 rows, the 1st and 3rd are similar, each has 3 cells: a text, a <span> </span> tag containing a number 1, and a slider. The 2nd row is an empty row of height 10px. The last two small stables contain a row of radio buttons and a row of buttons, respectively. <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> <style>.slidecontainer {width: 100%;.slider { -webkit-appearance: width: 100%; height: 5px; border-radius: background: outline: none; opacity: 0.7; 5px; #d3d3d3; -webkit-transition: transition: none;.2s; opacity.2s;.slider:hover { opacity: 1;.slider::-webkit-slider-thumb { -webkit-appearance: appearance: width: height: 25px; 25px; none; border-radius: 50%; background: cursor: #4CAF50; pointer; none;

7 .slider::-moz-range-thumb { width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer; </style> </head> <body background=blueback.jpg> <FONT face=arial color=#000080> <h2> Time Value of Money Solver </h2> <td>number of Payments: <td><input style="width:120px"> <td>interest Rate per Year: <td><input style="width:120px"> <td>% <td>present Value: $ <td><input style="width:120px"> <td style="width:5px"> <td>payment: $ <td><input style="width:120px"> <td style="width:5px"> <td>future Value: $ <td><input style="width:120px">

8 <tr> <td>number of Payments per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider"> </div> <tr style="height:10px"> <tr> <td>number of Compounding per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider"> </div> <td> <label>end-of-period Payments</label> <input type="radio">

9 <td> <label>beginning-of-period Payments</label> <input type="radio"> <td><button style="width:70px" type="button">solve</button> <td><button style="width:70px" type="button">reset</button> <td><button style="width:70px" type="button">closed</button> </body> </html> Finally we use a big table to group all the small tables together and give it a background color. <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> <style>.slidecontainer {width: 100%;.slider { -webkit-appearance: width: 100%; height: 5px; none;

10 border-radius: 5px; background: #d3d3d3; outline: none; opacity: 0.7; -webkit-transition:.2s; transition: opacity.2s;.slider:hover { opacity: 1;.slider::-webkit-slider-thumb { -webkit-appearance: none; appearance: none; width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer;.slider::-moz-range-thumb { width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer; </style> </head> <body background=blueback.jpg> <FONT face=arial color=#000080> <h2> Time Value of Money Solver </h2> <table bgcolor="#f9e79f"><tr><td align="center">

11 <td>number of Payments: <td><input style="width:120px"> <td>interest Rate per Year: <td><input style="width:120px"> <td>% <tr><td align="center"> <td>present Value: $ <td><input style="width:120px"> <td style="width:5px"> <td>payment: $ <td><input style="width:120px"> <td style="width:5px"> <td>future Value: $ <td><input style="width:120px"> <tr><td align="center"> <tr> <td>number of Payments per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider">

12 </div> <tr style="height:10px"> <tr> <td>number of Compounding per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider"> </div> <tr><td align="center"> <td> <label>end-of-period Payments</label> <input type="radio"> <td> <label>beginning-of-period Payments</label> <input type="radio">

13 <tr><td align="center"> <td><button style="width:70px" type="button">solve</button> <td><button style="width:70px" type="button">reset</button> <td><button style="width:70px" type="button">closed</button> </body> </html> We can also change the default style of the big table and give it a border. To do this, we first define a class named table1 in the <style> </style> tag, then ask the table to use this class. <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> <style>.slidecontainer {width: 100%;.slider {

14 -webkit-appearance: none; width: 100%; height: 5px; border-radius: 5px; background: #d3d3d3; outline: none; opacity: 0.7; -webkit-transition:.2s; transition: opacity.2s;.slider:hover { opacity: 1;.slider::-webkit-slider-thumb { -webkit-appearance: none; appearance: none; width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer;.slider::-moz-range-thumb { width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer; table.table1 {border: </style> </head> 15px outset grey;

15 <body background=blueback.jpg> <FONT face=arial color=#000080> <h2> Time Value of Money Solver </h2> <table class="table1" bgcolor="#f9e79f"><tr><td align="center"> <td>number of Payments: <td><input style="width:120px"> <td>interest Rate per Year: <td><input style="width:120px"> <td>% <tr><td align="center"> <td>present Value: $ <td><input style="width:120px"> <td style="width:5px"> <td>payment: $ <td><input style="width:120px"> <td style="width:5px"> <td>future Value: $ <td><input style="width:120px"> <tr><td align="center"> <tr> <td>number of Payments per Year: <td style="width:40px">

16 <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider"> </div> <tr style="height:10px"> <tr> <td>number of Compounding per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold">1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider"> </div> <tr><td align="center"> <td> <label>end-of-period Payments</label> <input type="radio">

17 <td> <label>beginning-of-period Payments</label> <input type="radio"> <tr><td align="center"> <td><button style="width:70px" type="button">solve</button> <td><button style="width:70px" type="button">reset</button> <td><button style="width:70px" type="button">closed</button> </body> </html> We now have the skeleton :

18 Next, we need to write some Javascript to do calculations. We first give names to all the dynamic fields, associate the labels of the radio button with the radio button so one can click the label too, give the 1st radio button a default value checked, group 2 radio buttons together with name="eb" so that only one of them can be checked, and add a <script> </script> tag. We will use the same name as in the problem 2 of Exercise 10 for each corresponding field. <!DOCTYPE html> <html> <head> <meta name="viewport" content="width=device-width, initial-scale=1"> <style>.slidecontainer {width: 100%;.slider { -webkit-appearance: width: 100%; height: 5px; border-radius: background: outline: none; 5px; #d3d3d3; none;

19 opacity: 0.7; -webkit-transition:.2s; transition: opacity.2s;.slider:hover { opacity: 1;.slider::-webkit-slider-thumb { -webkit-appearance: none; appearance: none; width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer;.slider::-moz-range-thumb { width: 25px; height: 25px; border-radius: 50%; background: #4CAF50; cursor: pointer; table.table1 {border: </style> </head> 15px outset grey; <body background=blueback.jpg> <FONT face=arial color=#000080> <h2> Time Value of Money Solver </h2> <table class="table1" bgcolor="#f9e79f"><tr><td align="center">

20 <td>number of Payments: <td><input id="n" style="width:120px"> <td>interest Rate per Year: <td><input id="r" style="width:120px"> <td>% <tr><td align="center"> <td>present Value: $ <td><input id="pv" style="width:120px"> <td style="width:5px"> <td>payment: $ <td><input id="pmt" style="width:120px"> <td style="width:5px"> <td>future Value: $ <td><input id="fv" style="width:120px"> <tr><td align="center"> <tr> <td>number of Payments per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold" id="ppyt" >1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider" id="ppy" >

21 </div> <tr style="height:10px"> <tr> <td>number of Compounding per Year: <td style="width:40px"> <span style="float:right;color:blue;font-size:15pt;font-weight:bold" id="cpyt" >1</span> <td style="width:20px"> <td style="width:250px"> <div class="slidecontainer"> <input type="range" min="1" max="12" value="1" class="slider" id="cpy" > </div> <tr><td align="center"> <td> <label for="ed" >End-of-Period Payments </label> <input type="radio" id="ed" name="eb" checked > <td> <label for="bg" >Beginning-of-Period Payments</label> <input type="radio" id="bg" name="eb" >

22 <tr><td align="center"> <td><button style="width:70px" type="button">solve</button> <td><button style="width:70px" type="button">reset</button> <td><button style="width:70px" type="button">closed</button> <script> </script> </body> </html> The corresponding term of Maple s procedure in Javascript is function. The functions ppyp, cpyp, and reset are almost identical to the procedures in problem 2 of Exercise 10. To see the similarities, we put them side-by-side. Here is the code for the function ppyp:

23 Javascript function ppyp() { ppyt.innerhtml = ppy.value; cpyt.innerhtml = ppy.value; cpy.value = ppy.value; ; Maple ppyp := proc () local a; a := Maplets:-Tools:-Get(ppy); Maplets:-Tools:-Set( ppyt = a, cpyt = a, cpy = a ) end: We also need to an Place the function ppyp inside the <script> </script> tag. oninput to the slider ppy so that this function will execute whenever ppy s value is changed: <input type="range" min="1" max="12" value="1" class="slider" id="ppy" oninput="ppyp()"> It is a good practice to write one function at one time, test it until it works properly, then write next. So save the file and refresh your browser. Drag the slide ppy to see if the function works properly. Here is the code for the function cpyp Javascript Maple function cpyp() { cpyp := proc () local b; cpyt.innerhtml = cpy.value; b := Maplets:-Tools:-Get(cpy); ; Maplets:-Tools:-Set( cpyt = b ) end: We also need to add an oninput to the slider cpy: <input type="range" min="1" max="12" value="1" class="slider" id="cpy" oninput="cpyp()"> Drag the slider cpy to make sure that the function works properly. Here is the code for function reset. It basically set everything to their default values. Javascript function reset() { n.value = ""; r.value = ""; pv.value = ""; pmt.value = ""; fv.value = ""; ppyt.innerhtml = 1; cpyt.innerhtml = 1; ppy.value = 1; cpy.value = 1; ed.checked = true; ; Maple reset := proc () Maplets:-Tools:-Set( n = "", r = "", pv = "", pmt = "", fv = "", ppyt = 1, cpyt = 1, ppy = 1, cpy = 1, ed = true ) end:

24 Add an onclick to the Reset button and test it. <button style="width:70px" type="button" onclick="reset()">reset</button> The function for calculations is named as TVM. Most parts of the function TVM is adapted from the Maple procedure TVM in problem 2 of Exercise 10 directly. Here is the code. function TVM() { var N = parsefloat(eval(n.value)); var R = parsefloat(eval(r.value)); var PV = parsefloat(eval(pv.value)); var PMT = parsefloat(eval(pmt.value)); var FV = parsefloat(eval(fv.value)); var PpY = parsefloat(ppy.value); var CpY = parsefloat(cpy.value); var s = 1; var y; var z; var v; var u = function (i) { return Math.pow(1+i/(100*CpY),CpY/PpY); ; if (ed.checked == true) { s = 0; ; if (N!== N && R == R && PV == PV && PMT == PMT && FV == FV ) { v = (PMT*((1-s)+s*u(R))/(u(R)-1)-FV)/(PV+PMT*((1-s)+s*u(R))/(u(R)-1)); if (PV*PMT >= 0 && PV*FV >=0 && PMT*FV >=0) { alert("cash flows in different directions need to have opposite signs!"); else if (v <= 0) { alert("check your data!");

25 else { y = Math.log(v)/Math.log(u(R)); n.value = y; else if (N == N && R!== R && PV == PV && PMT == PMT && FV == FV ) { var f = function (x) { return x*(((pmt*s+pv)*(n-1)*x*x+((n-s-2)*pmt-pv)*x-2*pmt) *Math.pow(1+x,N)+(1+x)*((PMT*s-FV)*x+2*PMT))/((N*(PMT*s+PV) *x*x+pmt*(n-1)*x-pmt)*math.pow(1+x,n)+pmt*(1+x)) ; if (PV*PMT >= 0 && PV*FV >=0 && PMT*FV >=0) { alert("cash flows in different directions need to have opposite signs!"); else { var j; z = -(N*PMT+FV+PV)/(N*(PMT*s+PV)); for (j = 0; j < 15; j++) { z = f(z); y = 100*CpY*(Math.pow(1+z,PpY/CpY)-1); r.value = y; else if (N == N && R == R && PV!== PV && PMT == PMT && FV == FV ) { y = -(PMT*(Math.pow(u(R), N)-1)*(1-s+s*u(R))/(u(R)-1)+FV)/Math.pow(u(R), N); pv.value = y; else if (N == N && R == R && PV == PV && PMT!== PMT && FV == FV ) { y = -(FV+PV*Math.pow(u(R), N))*(u(R)-1)/((Math.pow(u(R), N)-1)*(1-s+s*u(R)));

26 pmt.value = y; else if (N == N && R == R && PV == PV && PMT == PMT && FV!== FV ) { y = -PV*Math.pow(u(R), N)-PMT*(Math.pow(u(R), N)-1)*(1-s+s*u(R))/(u(R)-1); fv.value = y; else { alert("which one do you want to solve?"); ; Place it inside the <script> </script> tag, and add an onclick to the Solve button so that the TVM function executes whenever Solve button is clicked. We also add an onclick to Close button so that the Javascript function self.close() executes when the button is clicked. <button style="width:70px" type="button" onclick="tvm()">solve</button> <button style="width:70px" type="button" onclick="self.close()" >Closed</button> To understand the commands, we list side-by-side comparisons of some Javascript commands in the function TVM and corresponding Maple commends in the procedure TVM Javascript var N = parsefloat(eval(n.value)); Maple N := Maplets:-Tools:-Get(n::anything): var s = 1; if (ed.checked == true) {s = 0;; var u = function (i) { return Math.pow(1+i/(100*CpY),CpY/PpY); ; if ED = true then s := 0 else s := 1 fi: u := i ( ) CpY 1 PpY 1 + : 100 CpY

27 if (N!== N && R == R && PV == PV && PMT == PMT && FV == FV ) { else if (N == N && R!== R && PV == PV && PMT == PMT && FV == FV ) { else if (N == N && R == R && PV!== PV && PMT == PMT && FV == FV ) { else if (N == N && R == R && PV == PV && PMT!== PMT && FV == FV ) { else if (N == N && R == R && PV == PV && PMT == PMT && FV!== FV ) { else { alert("which one do you want to solve?"); if type(n, numeric) = false and (type(r, numeric) and type(pv, numeric) and type(pmt, numeric) and type(fv, numeric)) = true then elif type(r, numeric) = false and (type(n, numeric) and type(pv, numeric) and type(pmt, numeric) and type(fv, numeric)) = true then elif type(pv, numeric) = false and (type(n, numeric) and type(r, numeric) and type(pmt, numeric) and type(fv, numeric)) = true then elif type(pmt, numeric) = false and (type(n, numeric) and type(r, numeric) and type(pv, numeric) and type(fv, numeric)) = true then elif type(fv, numeric) = false and (type(n, numeric) and type(r, numeric) and type(pv, numeric) and type(pmt, numeric)) = true then else error "Which one do you want to solve?" fi: Javascrip s eval( ) function returns NaN (not a number) on a non-numerical input. We use this property to determine the variable to be solved because a variable with a value NaN is the only variable in Javascript not equal to itself. So we use variable!== variable to determine if variable = NaN. v = (PMT*((1-s)+s*u(R))/(u(R)-1)-FV)/ (PV+PMT*((1-s)+s*u(R))/(u(R)-1)); v := evalf ( P MT (1 s+s u(r)) F V u(r) 1 P MT (1 s+s u(r)) P V + u(r) 1 ) : The code for solving N:

28 if (PV*PMT >= 0 && PV*FV >=0 && PMT*FV >=0) { alert("cash flows in different directions need to have opposite signs!"); else if (v <= 0) { alert("check your data!"); else { y = Math.log(v)/Math.log(u(R)); n.value = y; The code for solving PV: y = -(PMT*(Math.pow(u(R), N)-1)*(1-s+s*u(R))/(u(R)-1)+FV) /Math.pow(u(R), N); pv.value = y; The code for solving PMT: y = -(FV+PV*Math.pow(u(R), N))*(u(R)-1) /((Math.pow(u(R), N)-1)*(1-s+s*u(R))); pmt.value = y; The code for solving FV: y = -PV*Math.pow(u(R), N) -PMT*(Math.pow(u(R), N)-1) *(1-s+s*u(R))/(u(R)-1); fv.value = y; if PV*PMT 0 and P V F V 0 and P MT F V 0 then error "Cash flows in different directions need to have opposite signs" elif v 0 then error "Check your data" else ( ) y := evalf ln(v) ; ln(u(r)) Maplets:-Tools:-Set(n = y) fi: y := evalf ( ) P MT (u(r) N 1) (1 s+s u(r)) +F V (u(r) 1) : u(r) N Maplets:-Tools:-Set(pv = y): ( y := evalf (F V +P V u(r)n ) (u(r) 1) (u(r) N 1) (1 s+s u(r)) Maplets:-Tools:-Set(pmt = y): ( y := evalf P V u(r) N ) : P MT (u(r)n 1) (1 s+s u(r)) u(r) 1 Maplets:-Tools:-Set(fv = y): ) : The only code completely different from the Maple procedure TVM is the code for solving R. Unlike Maple, Javascript does not have a built-in numerical equation solver like fsolve in Maple. So we have to make one. What we used is the Newton s method with fixed 15 iterations and with initial point to be the linear approximation. In Maple s TVM, we used fsolve to solve P V u(x) N + P MT (u(x)n 1) (1 s + s u(x)) u(x) 1 + F V = 0, for x, where u(x) = ( ) CpY i P py CpY

29 Let u 1 = z and g(z) = P V (z + 1) N + P MT ((z + 1)N 1)(1 s + s(z + 1)) z Then the iteration function for the Newton s method is given by With the help of Maple, we get f(z) = z g(z) g (z) + F V. f(z) = x((z2 (P MT s + P V )(N 1) + ((N s 2)P MT P V )z 2P MT )(1 + z) N + (z(p MT s F V ) + 2P MT )(1 + z) (Nz 2 (P MT s + P V ) + P MT (Nz z 1))(1 + z) N. + P MT (1 + z) Replace (1 + z) N (1 + z) N Nz, N x in the equation g(z) = 0 and solve z, we have an approximated solution which is the initial point of our iteration. The 15 iterations is performed by z N P MT + F V + P V N (P MT s + P V ), for (j = 0; j < 15; j++) {z = f(z); which is equivalent to Maple s code for j from 0 while j<15 do z:=f(z) od: The solution for R is given by y = 100*CpY*(Math.pow(1+z,PpY/CpY)-1); i.e. y = 100CpY ((1 + z) P py CpY 1 ). Please make the following calculations to verify that your program works properly. # of PMTS I PV PMT FV P/Y C/Y E/B Answer 48? E ? B ? 1 1 B ? E ? E

Exercise 10. Starting from this exercise, we will learn how to make a GUI, graphical user interface, in Maple.

Exercise 10. Starting from this exercise, we will learn how to make a GUI, graphical user interface, in Maple. Exercise 10 Starting from this exercise, we will learn how to make a GUI, graphical user interface, in Maple. 1) (50 points) The first GUI we will make is a Mortgage Payment Calculator. Open a new Maple