Investment Simulator (Arrays) You are encouraged to form a team of 2 or 3 to work on this homework. Each team submits only

one copy of the homework. Submit your homework on Blackboard before the deadline. No late

homework is accepted. Introduction

You probably have heard of the saying, “A penny saved is a penny earned”. Well, if you invest

your saved money wisely, a penny saved can be more than a penny earned. How much can it be?

In this homework, you will figure this out through simulation.

Suppose you are a disciplined investor. In the beginning of each month, you invest the same

amount of your saved money in selected funds. After 10 ten years, how much will be your

investment? This depends on two factors: the amount of your monthly investment, the monthly

return of your investment portfolio. For the monthly investment amount, you may consider

scenarios of different amounts, e.g., $50, $100, $500, and $1,000. For monthly return, well,

nobody would know because the market fluctuates all the time. But we can use simulated values

for the returns.

According to the article at https://www.ifa.com/articles/with_stock_returns_normally_

distributed/, historic monthly returns roughly have a normal distribution. For the simulation,

we assume that monthly return is drawn probabilistically from two normal distributions:

• 95% probability from N (1%, 2.5%)

• 5% probability from N (−4.5%, 2.5%)

You will be provided with a partially finished program. After adding your code to complete the

program, it will output the monthly rate of return and account balance for each saving scenario.

Below is a sample output. 1 Month Return

50

100

1

1.1696%

50.58

101.17

2

0.2533%

100.84

201.68

3

2.0974%

154.00

308.01

...

119

1.8881%

9,481.88

18,963.76

120

1.5656%

9,681.11

19,362.23

Average Monthly Return: 0.6426% 500

505.85

1,008.40

1,540.03 1000

1,011.70

2,016.79

3,080.07 94,818.81

96,811.13 189,637.61

193,622.25 Partially Completed Program

The program includes two helper methods to generate simulated monthly returns. You only need

to add code to the main method as instructed by the embedded comments.

import java.util. Random ;

public class InvestSimulation {

private static Random random = new Random ();

private static double nMean = -.045 , nStd =.025 , pMean =.01 , pStd =.025;

public static void main( String ... args ) {

int N =120; // for ten years (120 months )

double r = new double [N];

generateReturns (r);

// add your code here:

// use a 1-D array to hold monthly investment amounts (four scenarios )

// create a 2-D array for storing monthly balance (120 months , 4 scenarios )

// define a variable to store running total of monthly return

// use a nested loop to populate the 2-D array and output data.

}

public static double getGaussian ( double mean , double stddev ) {

return mean + stddev * random . nextGaussian ();

}

public static void generateReturns ( double r) {

for (int i=0; i<r. length ; i++) {

if (Math. random () <.05) { // negative return

r[i] = getGaussian (nMean , nStd);

} else {

r[i] = getGaussian (pMean , pStd);

}

}

}

} 2 Implementation Requirement

This program must be implemented by following the instructions included as comments in the

code provided above.

Here is a bit more information about how to calculate monthly balance. The balance at the

end of a given month depends on the balance at the end of the previous month, the investment

amount each month, and the rate of return of the given month. Let ai,j be the account balance

at the end of month i of the j–th investment scenario (monthly investment amount), ri be the

rate of return for month i, and mj be the amount of new investment in the beginning of each

month (e.g., 50, 100, etc) of the j–th investment scenario. Then we have

ai,j = (ai−1,j + mj )(1 + ri )

The values of the three variables are from three arrays. Pay special attention to the first

month, for which the previous month’s balance must be 0, i.e., the ai−1,j must be 0. If you let

i = 0 be the the first month, then the first month must be handled differently from the rest of

the months; if you let i = 1 be the first month, then you can calculate all months the same way

(but the array must have one extra row). Example code for choosing i = 0 to te the first month

is shown below:

if (i==0) {

data[i][j] = monthlyInvest [j ]*(1+ r[i]);

} else {

data[i][j] = (data[i -1][j] + monthlyInvest [j] )*(1+r[i]);

} Submission

Create your write-up using a word processor (e.g., Word). Make sure you include the following

parts:

• Title page. The title page should include the assignment information, your name (or team

member names), and a sentence summarizing what the program is about.

• Table of contents. List of all sections included in the submission. You do not need to have

page number for each section.

• The required sections of this assignment include:

– Overview. A brief description of the program: its function, input (the input is tuition

information hard-coded in the program), and output.

– Design and Implementation. A description of the design choices and structure of the

program: class, methods, variables, and other notable functions used (e.g., printf).

Include a flowchart for the generateReturns method. Also include a UML

class diagram of the class. You can create the class diagram using a table of the

word processor to separate the three sections.

3 – Testing. Include screenshots to show the function (e.g., output) of the program.

– Discussion. Include the following discussions as subsections:

∗

∗

∗

∗ Difficulties encountered and how you solved them.

Sources of help you used.

What did you learn in terms of programming?

What did you learn in terms of personal finance? Try to related to the annual

expense exercise.

∗ Any other lessons learned from the assignment.

– Source code. Include source code as text, not images. Include comments in the source