Option #1: Consumer Mathematics #1

Write a report that answers the following questions and meet the list of requirements that follows.

Each of the problems you will be solving requires using your calculator to solve a financial equation. In order to calculate answers correctly, it is important that you follow several important rules:

1. Follow the Order of Operations to solve complicated problems.
2. Attempt to solve equations without writing down intermediate values. If you must write down values, keep as many digits or decimal places as you can. Better yet, use the memory locations in your calculator to store intermediate values.
3. NEVER round intermediate calculations. Only round the final answer.

Several excellent videos that describe how to solve algebraic expressions using the Order of Operations Rules are available at mathispower4u.yolasite.com. After reaching the Mathispower4u site, click on the Algebra 1 Video Library link and find the Order of Operations section in the first column. The first twelve short videos will give you an excellent overview. The next twelve may also be helpful.

http://www.mathispower4u.com

The questions in this assignment involve calculations related to simple interest, compound interest, annuities, or mortgages. Your introduction should provide background information about these topics, describing their use and importance.

Questions:

1. Simple Interest: Jack borrowed money to finance his new business. Private investors offered Jack $28,000 of the $35,000 he needed.  To make up the difference, Jack secured a small business, simple interest loan. Jack’s loan was structured as an installment loan and required him to pay $297.50/month for 30 months. Calculate the amount financed, total installment price, the finance charge, and the interest rate. 
2. Annuity Payment: Bruce is saving money to open a Hispanic food franchise. He needs $15,000 in two years to make his down payment and is investing in an annuity yielding an annual interest rate of 7% compounded monthly. If the annuity requires that Bruce make monthly investments, what annuity payment must Bruce make to save $15,000?
3. Mortgage Financing: Samantha purchased a $129,000 home with 30-year term, 6% rate mortgage. At closing she paid a $10,000 down payment, requiring her to purchase private mortgage insurance (PMI) at a cost of $25 per month. Calculate Samantha’s monthly mortgage plus PMI payment.

Requirements:

• Your paper should be 2-3 pages in length and should cite and integrate at least one credible outside source.
• Include a title page, an introduction, a body, a conclusion, and a Reference list.
• The introduction should summarize the problem and state what approach and method will be applied to solve it.
• The body of your paper should answer the questions posed in the problem, explain how you approached and approached and answered the question or solved the problem, and for each question, show all steps involved. Writing equations in Word can be done (a) by using the Word equation editor, (b) or you may want to simply cut/paste the equations provided for you in the Consumer Math Equations document. This document contains interest and other financial equations formatted using the Word equation editor as well as instructions for using the equation editor.  Another option is (c) to write your equations by hand and paste images (in JPG or other compressed format) in the appropriate places in your paper.
• The conclusion should summarize your findings and what you have determined from the data and your analysis, with a broader or personal perspective in mind when applicable.
• As with all written assignments, provide in-text citations and a reference page.
• Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.
• Document formatting, citations, and style should conform to APA Requirements. In addition, the items noted in the “Good Writing Tips” section should be observed. Refer to the document (attached at the bottom of the page) Calculating Tree Height as an example of how the paper is to be formatted.

 

 

Running head: CALCULATING TREE HEIGHT Calculating Tree Height
Craig Storlie
MTH109 – Mathematical Explorations
Colorado State University – Global Campus
Dr. Al Gebrawiz
September 10, 2013 1 CALCULATING TREE HEIGHT 2
Calculating Tree Height The height of tall objects can be difficult to measure using direct measurement. It may
also be dangerous and lack accuracy. An alternative to direct measurement is available by
incorporating trigonometry and other direct measurements. In this assignment, the height of a
large tree was calculated using the trigonometric tangent function.
Methodology and Discussion
In this problem, the height of a large tree is unknown. The tree is standing on horizontal
ground and is 150 feet from Point A. The angle between the ground and the tip of the tree is 40°,
and is measured at Point A (Figure 1). The goal of this problem is to determine the height of the
tree using trigonometry. Point A 40°
150 feet Figure 1. Dimensions used to calculate tree height.
One portion of trigonometry deals with right angle triangles – those that contain a right,
or 90°, angle. The tangent function describes the tangent of an angle as equal to the length of the
side opposite of the angle divided by the length of the side adjacent to the angle (not the
hypotenuse). This relationship can be used to calculate the height of the tree shown in Figure 1.
tan 40° = 0.84= tree height
150 feet tree height
150 feet CALCULATING TREE HEIGHT 3 tree height =0.84 ( 150 feet )
tree height =126 feet Errors can arise from inaccurate estimates of the angular measurement. Table 1 shows the
errors that would occur if incorrect angular estimates were made in the problem solved in this
paper. Errors can be significant, and can be minimized through the careful use of a protractor or
other accurate sighting device.
Table 1
Results of Angular Measurement Errors in Calculating Tree Height
Angle
(degrees)
40 (actual)
45
50 Estimated Height
(feet) Error
(feet) Error
(%) 126
150
179 0
24
53 0
19
42 Note: Estimated Height is calculated using Estimated Height = tan Ө (150 feet).
The method described in this paper provides an accurate estimate of object height if right
angle geometry exists and if the horizontal distance and angle measurements are accurately
made.
Conclusions
Trigonometry is a powerful tool. In this assignment, the height of an object was
calculated given the distance an object was from a point and the angle measured between the top
of the object and the horizon. This method does not provide an accurate estimate if a right
triangle is not formed between the object and the horizontal plane, such as an object standing
vertically on sloped ground. However, other simple trigonometric methods exist that can be used
for more complicated geometries (Gebrawiz, 2013). CALCULATING TREE HEIGHT 4 CALCULATING TREE HEIGHT 5
References Gebrawiz, A. B. (2013). Trigonometric measurement methodology. Madison, WI: Bolt Upright
Publishing.

Consumer Math Equations
Listed below are four equations that you may need for your Module 3, Critical Thinking assignment.
These are not easy to create in Word, and are given here for you to copy and paste into your document.
The variables within these equations can be replaced with numeric values, as needed. This editing is
much simpler than creating your own equation.
However, you can also create your own equations. Word’s equation editor can be found in the Symbols
group of the Insert tab. Clicking the Equation button in the Symbols group will insert an equation box
into your document.
After inserting an equation box (or clicking on an existing equation box), the Equation Tools Design tab
will appear on the Ribbon. This tab contains symbols and structures that can be used to create
equations. Two commonly used equation structures are the “empty-box” symbols found by clicking the
Fraction or Script buttons in the Structures group.
Simple Interest I =Prt
Compound Interest r
A=P 1+
n nt ( ) Annuity [( ) ] r
R 1+
n
A=
r
n nt −1 Amortized Loan Payment P
R= ( nr ) r
1− 1+
n −nt ( )

Attachments:

• 1492656087-MTH109_CalcTreeHeight_Module03-3.docx
• 1492656087-MTH109_ConsumerMathEquations_Mod03.docx