Han invests $13,000 into a fund that combines stocks and bonds. The return varies from year...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Han invests $13,000 into a fund that combines stocks and bonds. The return varies from year to year. The balance at 5- year intervals is given in the table below 0 5 10 15 20 25 y (Balance / $1,000)| 13 14.5 16 18.2 19.9 22.3 The goal of this exercise is to find constants a and b such that the model y = ae best fits the data. In order to do that. we apply the natural logarithm to both sides of the model. This yields In y = In (ae) and using properties of logarithms In y In a + In e In y = In a + bt If we let Y= In y, c, Ina and c₂=b, the problem now reduces to finding the linear fit Y = C₁+C₂! If we let y = In y, c₁ = Ina and c₂ = b, the problem now reduces to finding the linear fit Y = C₁ + c₂l to the set of data points 10 5 10 15 20 25 Y In (13) In (14.5) In (16) In (18.2) In (19.9) In (22.3) Part (a) • The vectors t and y have already been created for you. Compute the vector Y by evaluating the natural logarithm of y (note that the natural logarithm is entered as log in MATLAB). Create the matrix X for the linear fit Create the vector z Create the matrix s Find the cholesky decomposition of S and store it in U ▪ Solve the triangular system Uw = z using the backslash command. ▪ Solve the triangular system Uc = w using the backslash command Compute the best fit (use q = t) I • Plot the data points and Y (upper case Y) (Use 'o' to plot points) Plot the fit together with the original data points. Use 'linewidth', 2 and axis tight in your plot (Use '-' linestyle and color the line black) ▪ Release the figure by typing hold off Part (b) ▪ Compute a = ¹ and b = c₂ (where c, and ₂ are the values you found in part (a)). Store the values in the variables a and b respectively. . Enter figure to open a new figure. plot the original data points and y (lower case y) (Use 'o' to plot points) • Define a vector q that starts at 0 and ends at 25 with increments of 0.1. . Use the vector q to compute the exponential fit y=ae and store it in the variable fitz ▪ plot fit2 vs q together with the original data points. (Use red color to plot the line) Part (c) Use the linear model and the values of c, and c₂ computed in part (a) to determine the value ofr when the balance will reach $30,000. Store the result in the variable T. Hint: Note that y represents the balance in thousand of dollars and Y = In y. What should you substitute for Y in the linear fit to represent a balance of $30,000? Make sure you click on Run Script before you submit so you can check for syntax errors. Don't forget to include your name in the first editable line of the script. Han invests $13,000 into a fund that combines stocks and bonds. The return varies from year to year. The balance at 5- year intervals is given in the table below 0 5 10 15 20 25 y (Balance / $1,000)| 13 14.5 16 18.2 19.9 22.3 The goal of this exercise is to find constants a and b such that the model y = ae best fits the data. In order to do that. we apply the natural logarithm to both sides of the model. This yields In y = In (ae) and using properties of logarithms In y In a + In e In y = In a + bt If we let Y= In y, c, Ina and c₂=b, the problem now reduces to finding the linear fit Y = C₁+C₂! If we let y = In y, c₁ = Ina and c₂ = b, the problem now reduces to finding the linear fit Y = C₁ + c₂l to the set of data points 10 5 10 15 20 25 Y In (13) In (14.5) In (16) In (18.2) In (19.9) In (22.3) Part (a) • The vectors t and y have already been created for you. Compute the vector Y by evaluating the natural logarithm of y (note that the natural logarithm is entered as log in MATLAB). Create the matrix X for the linear fit Create the vector z Create the matrix s Find the cholesky decomposition of S and store it in U ▪ Solve the triangular system Uw = z using the backslash command. ▪ Solve the triangular system Uc = w using the backslash command Compute the best fit (use q = t) I • Plot the data points and Y (upper case Y) (Use 'o' to plot points) Plot the fit together with the original data points. Use 'linewidth', 2 and axis tight in your plot (Use '-' linestyle and color the line black) ▪ Release the figure by typing hold off Part (b) ▪ Compute a = ¹ and b = c₂ (where c, and ₂ are the values you found in part (a)). Store the values in the variables a and b respectively. . Enter figure to open a new figure. plot the original data points and y (lower case y) (Use 'o' to plot points) • Define a vector q that starts at 0 and ends at 25 with increments of 0.1. . Use the vector q to compute the exponential fit y=ae and store it in the variable fitz ▪ plot fit2 vs q together with the original data points. (Use red color to plot the line) Part (c) Use the linear model and the values of c, and c₂ computed in part (a) to determine the value ofr when the balance will reach $30,000. Store the result in the variable T. Hint: Note that y represents the balance in thousand of dollars and Y = In y. What should you substitute for Y in the linear fit to represent a balance of $30,000? Make sure you click on Run Script before you submit so you can check for syntax errors. Don't forget to include your name in the first editable line of the script.
Expert Answer:
Related Book For
Corporate Finance
ISBN: 978-0071339575
7th Canadian Edition
Authors: Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Gordon Ro
Posted Date:
Students also viewed these mathematics questions
-
Find constants A and B such that the function y = A sin x + B cos x satisfies the differential equation y" + y' - 2y = sin x.
-
The data given in the table below are the midterm scores in a course for a sample of 10 students and the scores of student evaluations of the instructor. (In the instructor evaluation scores, 1 is...
-
The density for X is given in the table of Problem 7. (a) Find E[X] (b) Find E[X - ] (c) Find Var[X] (d) Find the standard deviation for X.
-
Pinduoduo plans to launch a new platform to compete with its competitors, JD.Com, Taobao, and Tmall. The product manager of the new platform should decide whether to leverage the social commerce...
-
The following are the major balance sheet classifications:Current assets (CA) .................. Current liabilities (CL)Long-term investments (LTI) ............ Long-term liabilities (LTL)Property,...
-
Draw the hierarchy chart and design the logic for a program for the River Falls Homes Construction Company. Design a program that prompts the user for a lot number in the River Falls subdivision and...
-
Recognized limitations of financial statement analysis include each of the following except: a. companies in the same industry using different accounting methods. b. inflation. c. different levels of...
-
Johnson, president of the First National Bank of A, believes that it is appropriate to employ only female tellers. Hence, First National refuses to employ Ken Baker as a teller but does offer him a...
-
The Dauten Toy Corporation currently uses an injection molding machine that was purchased prior to the new tax legislation. This machine is being depreciated on a straight - line basis, and it has 6...
-
On December 31, 2021, the end of its first year of operations, Botani Associates owned the following securities that are held as long-term investments. On this date, the total fair value of the...
-
The current marketing trend has stressed the importance of creating an omnichannel presence for our consumers. Please compare and contrast multichannel marketing and omnichannel marketing methods....
-
The Western Farm Supplies Inc. chief executive officer ( CEO ) has asked you to compare the company s profit performance and financial position with the averages for the industry. The CEO has given...
-
Jeanne is currently taking the college course "Intro to Biology". The instructor often gives quizes. Of the past five quizzes, Jeanne got the following scores: 16 10 9 14 12. Find the standard...
-
Under Working Capital Management and Debt What are some of the advantages and disadvantages of short-term vs long-term debt? What are some actions a firm can take to shorten its cash? Public and...
-
Q1 Question 2 (6 points) On 1/1/2023 Hatch Inc. acquired 100% assets of Stewart Com and paid $500,000 cash Below includes the information of assets and liabilities of Stewart Com right before the...
-
Income Statement Completing this activity will help you learn to: Determine total revenues, expenses, and net income for a period and compare results over time. Extract information from a data set...
-
The graph of a function f is given. Sketch the graphs of the following transformations of f. y 5 -4 -2 2 4 6 5 00 8 10 10 x
-
If the amplifier indicated by the box input impedance of oo, which of the following statements are true ? has an open loop gain as well as Feedback factor (\beta = 1/ R_1\) The feedback is voltage...
-
ABC Company is considering purchasing manufacturing equipment from two different suppliers. Equipment A has a purchase price of $2.9 million and will cost $80,000, pre tax, to operate on an annual...
-
Air Canada, West Jet, and Transat A.T. Inc. announced purchases of planes on July 18 (18/7), February 12 (12/2), and October 7 (7/10), respectively. Given the following information, calculate the CAR...
-
Evan Inc. has offered $620 million cash for all of the common stock in Tanner Corporation. Based on recent market information, Tanner is worth $585 million as an independent operation. If the merger...
-
You have the following details for A. Bird of transactions with customers and suppliers. (a) 1 June credit purchases of 8,000, 6,000 and 5,000 from Robin, Falcon and Sparrow, respectively. (b) 4 June...
-
From the following accounting figures show the six steps in the accounting equation: opening assets 25,000, opening liabilities 25,000 (15,000 third party and 10,000 equity), profit 15,000 (income...
-
In this exercise we explore how the early stopping of the gradient descent iterations (see Example B.10), \[ \boldsymbol{x}_{t+1}=\boldsymbol{x}_{t}-\alpha abla f\left(\boldsymbol{x}_{t} ight), \quad...
Study smarter with the SolutionInn App