Signature Assignment. Course. MATH 1324: Math for Business and Social Sciences. Outcomes/Rubrics to be Assessed by the Assignment

Transcription

1 Signature Assignment Course MATH 1324: Math for Business and Social Sciences Assignment Title MATHEMATICAL REASONING EXERCISE Assignment ID Kevin Pinegar Outcomes/Rubrics to be Assessed by the Assignment o o o Communication Critical Thinking Empirical and Quantitative Reasoning Assignment Description Important Submission Instructions to the Student: 1. All explanations must be typed. The supporting math work must be neat and suitable for copying or scanning. The final document should be saved and submitted as a single.pdf file. 2. Give the assignment the heading GEN ED ASSESSMENT: MATH Do not include your name in the assignment or in the file name. 4. Submit your assignment to your instructor via Blackboard by the deadline established by your instructor. GENERAL EDUCATION COMMON ASSIGNMENT FOR MATH 1324 Scott wants to purchase a Toyota Rav4 XLE. The model he wants is available for $26,789. Scott has saved $4,000 for a down payment, and the dealer has offered $3,500 for his trade-in. He is considering three financing options. Toyota s financial department is offering 0% interest for three years Scott s credit union is offering 1.98% compounded monthly for four years His bank is offering 2.97% compounded monthly for five years Your Assignment: (a) What would Scott s monthly loan payment be for each option? (b) What total amount of interest would Scott pay for each option? (c) Describe the advantages and disadvantages of each financing option. (d) If you were Scott, which of these three financing options would you use and why?

2 GE Common Assignment Key Math 1324 Reasoning Exercise Scott wants to purchase a Toyota Rav4 XLE. The model he wants is available for $26,789. Scott has saved $4,000 for a down payment, and the dealer has offered $3,500 for his trade-in. He is considering three financing options. Option 1: Toyota s financial department is offering 0% interest for three years Option 2: Scott s credit union is offering 1.98% compounded monthly for four years Option 3: His bank is offering 2.97% compounded monthly for five years Your Assignment: (a) What would Scott s monthly loan payment be for each option? Prior to determining the monthly payments, the learner must find the amount financed by subtracting the down payment and trade in value from the list price. {26, = 19289} Option 1: There is no interest charge for this option, therefore the learner divides the total by 36 months. Answer: = $ Option 2: The learner must use the present value amortization formula given below. Given values are PV=19289, i=0.0198/12 and n=48 months. = ( i) ( /12) PMT PV = = $ n 48 1 (1 + i) 1 ( /12) Option 3: The learner must use the present value amortization formula given below. Given values are PV=19289, i=0.0297/12 and n=60 months. = ( i) ( /12) PMT PV = = $ n 60 1 (1 + i) 1 ( /12) (b) What total amount of interest would Scott pay for each option? The interest for each option is the sum of all payments less $ Option 1: This one is given as $0 since the rate is 0%. Option 2: 48(418.31)-19289=$ Option 3: 60(346.34)-19289=$ (c) Describe the advantages and disadvantages of each financing option. Option 1: Advantages are $0 interest charged. Disadvantage is that there is a higher monthly payment than the other two options. Option 2: Advantage is a lower payment than option 1. Disadvantage is it requires paying interest. Option 3: Advantage is the payment is the lowest of the other two options. Disadvantage is it requires paying the more interest than other two options. Note: It is ok if learners state the longer terms are disadvantages for the latter options but the main advantages/disadvantages are the interest charged and amount of the monthly payment. (d) If you were Scott, which of these three financing options would you use and why? The answer here will vary dependent upon the learner s personal preference. Although the reason should be consistent with the facts listed in part c.

3 Assignment Design Worksheet: Written Communication Course MATH 1324 Assignment Title MATHEMATICAL REASONING EXERCISE Assignment ID (to be assigned) Criterion Context of and Purpose for Writing Content Development Genre and Disciplinary Conventions Design (How does the assignment ask students to perform in the manner expected by the criterion?) Successful learners will compare three options for purchasing an automobile.. Successful learners will calculate monthly car payments for each option and discuss the advantages and disadvantages of each option. Unsuccessful learners will calculate incorrect values for monthly payments. Successful learners will calculate the interest charged for each option (part b) Unsuccessful learner will calculate incorrect interest amounts (part b) The final question requires the learner to choose an option and provide a written explanation for their choice. Unsuccessful learners will not provide advantages/disadvantages for each option. Unsuccessful learner will not provide reasons for the option selected. Successful learner will subtract the down payment and trade in value from the list price to find the amount financed before doing further calculations. Unsuccessful learners will not subtract the down payment and trade in value prior to future calculations. Successful learner will calculate option 1 simply by dividing the amount financed by 36. Successful learner will use the present value formula to determine the payments on Options 1 and 2. Unsuccessful learners will not use the appropriate method of calculating monthly payments. Successful learners will calculate the interest charged by taking the difference between the total payments and the amount financed. Successful learner will recognize that Option 1 requires the highest payment for the lowest term, but charges the least in interest charges. Successful learner will recognize that options 2 and 3 require higher interest charges and longer terms. Unsuccessful learners will not identify the higher payments payments for the shorter terms. Unsuccessful learners will not calculate to correct interest charges. Unsuccessful learners will not relate larger interest charges with longer terms and higher interest rates. Successful learners use sentences and mathematical formulas where appropriate to describe their results.

4 Sources and Evidence Successful learners will calculate the correct monthly payments for each option. Unsuccessful learners will calculate incorrect values for monthly payments. Control of Syntax and Mechanics Readability of Visual Elements Relevance, Accuracy, and Integration of Visual Elements A successful learner shows work that computes the amount finance as well as for each payment calculation. A successful learner will calculate the correct interest charges for each option. An unsuccessful learner may not use the correct value for the amount financed even though the other calculations use correct formulas. An unsuccessful learner may use the correct amount financed, but use incorrect formulas or values in the payment calculations. Unsuccessful learners will incorrectly calculate the interest charges for each option. A successful learner uses present value formulas when determining monthly payments and will use correct methods for calculating total interest charged. An unsuccessful learner may not use the present value formulas to calculate monthly payments (options 1 and 2). Unsuccessful learners will calculate all monthly payments by simply dividing the amount financed by the number of months. Unsuccessful learners will not calculate correct interest charges. A successful learner integrates their answers from parts a-b as evidence of their answers for parts c-d. An unsuccessful learner will not integrate answers from part a-b as evidence of their answers for parts c-d.

5 Assignment Design Worksheet: Critical Thinking Course MATH 1324 Assignment Title MATHEMATICAL REASONING EXERCISE Assignment ID (to be assigned) Criterion Explanation of Issues Design (How does the assignment ask students to perform in the manner expected by the criterion?) A successful learner will compare three options for purchasing an automobile by calculating monthly car payments for each option. A successful learner will compute the amount of interest charged for each option. A successful learner will discuss the advantages and disadvantages of each option and select an option with written explanation for their choice. Evidence Influence of Context and Assumptions Student s Position A successful learner will determine the amount financed and apply that amount to each of the monthly payment options. Learners will use the amortization (payment) formula to calculate monthly payments for options 2 and 3. (For option 1, the learner will divide the amount financed by 36.) A successfully learner will provide evidence of calculating total interest charges for each option by finding the difference between the sum of payments and the amount financed. The unsuccessful learner will not apply the given discounts to determine the amount financed. The unsuccessful learner will not provide evidence of the correct formulas used in calculating the monthly payments and interest charges. Successful learner will recognize that as the monthly payments decrease, the total interest charged increases. Successful learner will recognize that as interest rates increase the total interest charged increases. The unsuccessful learner will not state the above assertions. Successful learner must read the assignment, perform required calculations and make choices based on their critique of their current situation. Conclusions and Related Outcomes 1) The successful learner will recognize that option 1 charges no interest fees yet requires the highest monthly payment. 2) The successful learner will recognize that option 2 charges a lower interest charge than option 3, yet requires a higher monthly payment than option 3. 3) The successful learner will recognize that option 3 charges the most interest fees yet requires the lowest monthly payment. 4) The successful learner will recognize that higher interest charges are associated with higher interest rates and longer terms.

6 Assignment Design Worksheet: Empirical & Quantitative Reasoning (EQR) Course Math 1324 Assignment Title MATHEMATICAL REASONING EXERCISE Assignment ID Criterion Interpretation (to be assigned) Design (How does the assignment ask students to perform in the manner expected by the criterion?) A successful learners will perform calculations in part a in order of the options given. Once calculations are completed, successful learners will interpret the total interest charges for each option and list advantages/disadvantages for each option. Representation A successful learner will calculate the monthly payments and total interest charged for each option prior to stating the advantages and disadvantages. Calculation or Transformation 1) Compute the amount financed which is the list price less down payment and trade-in value =$19,289 2) Option 1: Calculate the monthly payment at 0% APR for 36 months. For this option, the learner should simply divide the balance by 36. $19,289/36=$ ) Option 2: Calculate the monthly payment at 1.98% APR for 48 months. PMT=19289(0.0198/12) / (1-( /12) -48 )= $ ) Option 3: Calculate the monthly payment at 2.97% APR for 60 months. PMT=19289(0.0297/12) / (1-( /12) -60 )=$ Application/Analysis 1) The students apply their understanding of interest charges versus lower monthly payments in order to make the best choice for their needs. 2) The advantage for Option 1 is no interest charges and shorter term with disadvantage being a higher monthly payments. The advantage for Options 2 and 3 are lower payments. The disadvantages are they require the purchaser to pay more in interest charges over longer terms. Assumptions A successful learner will not make assumptions outside of the information given. All pertinent values are given in the question. Formatted: List Paragraph, Numbered + Level: 1 + Numbering Style: 1, 2, 3, + Start at: 1 + Alignment: Left + Aligned at: 0.25" + Indent at: 0.5" Formatted: List Paragraph, Numbered + Level: 1 + Numbering Style: 1, 2, 3, + Start at: 1 + Alignment: Left + Aligned at: 0.25" + Indent at: 0.5" Communication Successful learners are required to communicate their answers using mathematical formulas and to write their final analysis using correct grammar.

7 Unsuccessful learners will not identify their answers. Unsuccessful learners will use incorrect mathematical formulas or write sentences that are not grammatically correct.