For example, if Company XYZ is trading for $25 and the XYZ 20 call option is trading at $7, then we would say that the option has an intrinsic value of $5 ($25 - $20 = $5), and a time value of $2 ($7 - $5 = $2). Options that have zero intrinsic value are comprised entirely of time value. Why Does Time Value Matter? Now that you can calculate the TVM (time value of money), it’s time to look at risk and return. From example 1, we know that you would need to save a whopping $2,308 per month to get from $0 to $1,000,000 in 20 years with a 6% growth. If you’re like me, that number seems pretty high.

Time Value Of Money Answers
Real World Example Of Time Value Of Money

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Word problems are a problem. Students of all levels continually struggle with word problems; however, there is a solution to this 'problem'. The objective for this curriculum unit is to show students the multiple ways that system of equations can be used to solve real-world problems. In order for students to be engaged and interested in learning, they need to see the real-world practicality behind the math concept being learned. Without a lot of practice, System of Equations can be difficult for students to compute correctly and efficiently. When difficulty is combined with a lack of interest or a question of relevance, the student can become frustrated and disengaged. Therefore, in order to capture the attention and interest of my students, I will first discuss what a system of equations is and then explain how to solve one using three different methods. Utilizing the substitution method, addition/subtraction elimination and multiplication/elimination methods, we will review how to solve a system of equations.

Once the students understand those concepts, I will discuss and review I = Prt and d = rt. Using the simple interest formula, I = Prt, the students will be exposed to how their money can grow in a year. This will undoubtedly be of interest to any student. The students will also be able to see the advantage and real-world practicality of calculating the distance an object can travel, given the rate of speed and time using the d = rt formula. Then I will combine the distance and interest formulas together with a system of equations and demonstrate how to solve real-world scenarios and exciting problems. I will also provide practical examples of problems involving wind and water currents, chemistry problems involving mixtures and solutions, more interest problems involving the time value of money, and other practical examples that involve systems of equations. I will spend two days on each of the three methods. Next, I will spend another three or four days introducing the interest and distance formulas, incorporating them into system of equations. It is critical that the students get a feel for solving the problems before I introduce the more complicated word problems. The distance formulas and simple interest formulas are not extremely complicated, and my students typically pick up on them quickly. I have also introduced them earlier in the year and use them as warm-up problems several times per week.

The first system of equations I will introduce is one that will require the substitution method to solve. For example;

y = 4x 3x + 4y = 36

A word problem that can be solved by the substitution method is;

'Teddy has 8 more songs on his iPod than Tyler. Together they have 112 songs. How many songs does each person have?'

Another example of a system of equations solvable by substitution is;

x + 3y = 9 2x - 5y = 27

The next class of systems of equations that I will present are solvable by the addition/subtraction method. An example would be;

2x + 4y = 33 2x + 6y = 54

In this system, the coefficient of x is the same in both equations. Therefore, if we subtract the first equation from the second equation we will be able to isolate the y variable. A word problem that would require the use of the addition/subtraction method would be;

'Teddy cuts grass in the summer for $ 20 a lawn. His neighbor, Gavin is very competitive and decides to cut grass as well but only charges $ 18 a lawn. Their total combined revenue one summer was $ 348. Teddy made $ 132 more than Gavin. How many lawns did they each cut?'

The last type of system of equations that I will speak of is one that requires the multiplication elimination method. An example of this type of system is;

3x + 6y = -6, 5x - 2y = 14.

An example of a word problem that we could use the multiplication elimination method to solve is:

'The air-mail rate for letters to Europe is 45 cents per half-ounce and to Africa as 65 cents per ounce. If Shirley paid $ 18.55 to send 35 half-ounce letters to Europe and Africa, how many did she send to Africa?'

This is just a brief overview of the types of problems that I will cover with my class in this unit.

I teach 8th grade Algebra in a suburban middle school in Charlotte, North Carolina. In this particular class, I have relatively few behavior problems. Talking at inappropriate times is my students' biggest fault. Carmel Middle School is on a block schedule and my Algebra class meets every day for approximately 85 minutes. I have a pacing guide, created by the county I teach in, that I follow. There is not an abundance of time allocated for systems of equations, so I tend to move rather quickly. I typically have about 30 students in an Algebra class and I have approximately 20 to 25 students in my lower level classes.

The population at my school is as follows: 61.4 % Caucasian, 21.5% African American, 11 % Hispanic and 4 % Asian. Twenty six percent of our students are enrolled in the Gifted and Talented program, while 12.6% of our students have some degree of disability. We have 30% of our population on free or reduced lunch and the other 70% pay or bring bag lunches.

The percent of students at or above grade level in math is 80%, and the students at or above grade level in reading is even higher- 91.5%. These percentages put us above the Charlotte Mecklenburg District average in both categories. For the last few years, Carmel Middle School has consistently had 100% of Algebra and Geometry students performing at or above grade level.

The District itself is growing larger and larger every year; it currently enrolls 122,000 students and employs 10,050 teachers. Over the last couple of years, the Charlotte-Mecklenburg School System has increased the number of students by approximately 6,000 students per year. The district population is 43% African American, 37% Caucasian, 12% Hispanic, and 4% Asian.

First, I will start with introducing the three ways to solve a system of equations. The first way is called the substitution method. I spend two days on substitution with my class. Typically, the problems are set up such that there is only one variable on each side of the equation and at least one variable has a leading coefficient equal to one. The other equation has two variables, as well, each on the same side of the equation. An example is as follows:

x = 3y, 2x + 4y = 20.

Equations in the above form are the simplest and easiest way to start a substitution problem. The students need to understand that when there is more than one unknown in an equation, it cannot be solved as is. Since x = 3y, we can simply 'substitute' the 'x' variable in the second equation. This would produce the equation 2(3y) + 4y = 20. I ask for a volunteer to tell me if we now have more than one unknown variable. The rest of the equation should be solved easily. The students know how to solve multi-step equations by combining like terms with relative ease at this point. I make sure also to plug in my answer for 'y' and solve for 'x,' as well. The students need to see that it does not matter which equation they plug the value of 'y' into. They will get the same value of 'x' regardless.

I would also demonstrate problems where the variables are on the same side for both equations, but again one of them has a leading coefficient equal to one. For example:

x - 7y = 21 x + 2y = 14.

I would demonstrate how easy it is to place the first equation, x - 7y = 21, in the form x = 7y + 21, and then substitute the value of x into the second equation and solve. The students could have also set the second equation, x + 2y = 14, equal to 'x' by subtracting '2y' from both sides to get x = -2y + 14. It is

Real World Example Of Time Value Of Money