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MATH 141 – Capstone Project

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In this project, you will consider the purchase of a new vehicle (latest model). You will write a

professional report using appropriate technology and will apply mathematical skills and

techniques learned in class to help you evaluate your purchasing decisions as well as different

financing options.

In part I of this project, you will collect real life-data and use it to model the resale value of your

chosen car over time. Part II of the project will focus on considering different options of

financing the car such as choosing the length of the loan or reducing interest payments.

Guidelines for Being Successful:

 Read and follow instructions carefully

 Review the grading rubric carefully to ensure that you are familiar with the expectations

for each section

 If you need clarification about any part of this project, please be sure to ask your

instructor in a timely manner

o Ten percent will be deducted for each calendar day the project is submitted after

the due date.

o A project is considered as “submitted” when it is available to the professor to

view in Canvas. After you submit the project, please open it up in Canvas to

ensure it is readable

o No credit is given for projects submitted after five days after the due date (2

calendar days for winter/summer terms)

 Submit a neat professional report typed (double-spaced) using your choice of word

processing software. The use of appropriate technology is expected throughout the


o All mathematics must be typed using mathematical notation package and all

graphs, charts and diagrams must be created using a mathematical or statistical

software package

o All graphs must be “complete” and embedded into the report. Hand-drawn

graphs or graphs submitted in a separate document will not be accepted

 Group work is not allowed for this project. While you may discuss your ideas with

others, each student must submit his or her own original work.

Getting Help:

 You may discuss the project with others and may consult any available resource

(including your instructor, classmates, LAC and HR230 tutors, or the Internet) provided

that the computations, explanations and graphs in your project are your own original


 You must cite all of your resources using APA format

 If you need help with writing, use the HCC Writing Center: For further information, see

the HCC Web page under the heading “Writing Center” or call the Writing Center at

(443) 518-4101. PGCC students at the Laurel College Center should see the PGCC

Writing Center for assistance.

Guidelines for Submission:

 Submit your project via the Canvas link as a PDF file

 VeriCite will be used as a deterrent for plagiarism. This program is integrated into the

Canvas submission process. All submissions will be compared against the VeriCite

database and receive an “originality” rating. To avoid a false flag in VeriCite, do not

copy and paste the instructions/questions into your final submission

Part II – Financing a Car

In Part II of the Capstone Project, you will consider different options of financing your new car.

You will create and analyze the amortization schedule for your chosen loan and discuss how to

reduce the total interest and the length of your loan.

This is a research paper and should be written as a narrative.

Introduction (16 points):

 Provide the make, model and MSRP of your chosen car (2 pts)

 Provide the name, address and contact information of two local dealerships that sell

your car (with the features chosen in Part I of the project). Remember that you are

buying a new car (latest model) and hence do not use used car dealerships! (2 pts)

 Provide the Dealer Incentive for the car from each of the two dealerships. (Dealer

Incentive is a financial inducement used by manufacturers to motivate dealers to sell a

particular product by offering discounts on that product (a price lower than the listed

MSRP. A dealer incentive may also take the form of a cash incentive, such as a rebate,

awarded directly to the consumer) Based upon the Dealer incentive and/or other

contributing factors, decide from which dealership you will purchase your car. (Explain

your decision) (4 pts)

 Decide whether you would make a down payment on your car and state the amount (2


 If you are currently driving a car, find out the Trade-in Value of your current car and

decide whether you would want to trade it in upon purchasing the new car. You may

also decide not to trade-in your car, but you must explain your decision (such as passing

your current car to your teenage child, etc.) (2 pts)

 Calculate the amount financed. (This is the amount for which you will take a car loan. It

should consist of the dealer’s price –(down payment, trade-in vale, and any other

applicable incentives) (4 pts)

Considering Different Loan Options (9 points):

Car loan rates vary based on one’s credit score, term length of the loan and other factors

relevant to a lender’s risk in offering the loan. The annual percentage rate (APR) typically ranges

from 3% to 10%. In this project we will consider the following term lengths and APR’s:

Term length of the loan (in months)

36 48 60

APR (%)

3.71 3.81 3.93

 Using the amount financed for your car, calculate

o the monthly payment (PMT) (3 pts)

o the total amount paid over the length of the loan (3 pts)

o the total amount of interest paid over the length of the loan (3 pts)

for all three loans listed above. (Organize this information in a table)

 Choose one of these loans and justify your decision

 Create an amortization schedule for the chosen loan only. The schedule must be

embedded in your report and must include the following columns (6 pts):

o Payment Number

o Monthly Payment (PMT)

o Interest (I)

o Unpaid Balance Reduction (UBR)

o Unpaid Balance

Linear Regression Models I(x) and UBR(x) (22 points):

 Use technology to calculate the linear regression equation ( )I x where I is the interest

in dollars listed in the Interest column (I) of your amortization schedule and x is the

payment number. Round your figures to two decimal places (5 pts)

 Use technology to create the graph of ( )I x . Your graph must be a complete graph:

o The graph has a title (2 pts)

o Each axis is labeled with its variable (2 pts)

o Each axis is labeled with a subtitle (2 pts)

o Each axis shows appropriate tick marks and scaling (2 pts)

o Each line, curve or function is clearly drawn and labelled with its equation. A

legend may be used when appropriate. Equations must be professionally typed

using correct mathematical notation(2 pts)

o Vertical and horizontal intercepts are shown on the graph (2 pts)

o Incorporate your graph into your report in a smooth, professional way. Hand-

drawn graphs or hand-written description will not be accepted. Graphs

submitted in a separate document will not be accepted

 Use technology to calculate the linear regression equation ( )UBR x where UBR is the

unpaid balance reduction in dollars listed in the UBR column of your amortization

schedule and x is the payment number. Round your figures to two decimal places (5 pts)

 Use technology to create the graph of ( )UBR x . Your graph must be a complete graph

having all of the features listed for the graph of ( )I x

Discussion (22 points):

1. Using your linear regression equation for ( )I x , find the slope and interpret its meaning

within the context of the model (5 pts)

2. Using your linear regression equation for ( )UBR x , find the slope and interpret its

meaning within the context of the model (5 pts)

3. Discuss the relationship between the two slopes (3 pts)

4. Discuss at least three different options of paying the loan faster. (These must be all

sensible and financially sound options such as rounding up your monthly payment or

making an extra payment every year. Saying that you would slap the amount on credit

card or borrow the money from a friend does not constitute a sensible and financially

sound option.) Discuss the following for each of the options:

o Describe how you are going to shorten the loan (3 pts)

o Calculate by how much will the term of your loan be shortened (3 pts)

o Calculate the new total interest paid over the length of the loan (3 pts)



The car chosen for this paper is the 2018 Ford Fiesta. The make is Ford, and the model is the Fiesta. The MSRP (Manufacturer’s Suggested Retail Price) of the car for this year is $15,363. The key features for this car include performance, safety, the interior design, and reliability. On performance, the base engine is powerful together with its sharp handling as well as accurate steering. The ride is bumpy over uneven surfaces. The car has a standard 1.6-litre four-cylinder engine which generates 120 horsepower as well as adequate acceleration. Also, the car’s standard five-speed manual gearbox is easy to use. Thus, the car is good to use in bumpy or rough surfaces. According to the J.D. Power and Associates Vehicle Dependability Study (VDS) rating, the car is very reliable. The car has no history of safety recalls which are issued by NHTSA. Also, the car has a 36,000 mile or three years limited warranty as well as a 60,000 mile or five-year powertrain warranty (Kelley Blue Book Co. 2017).

According to National Highway Traffic Safety Administration safety ratings and Insurance Institute for Highway Safety crash test ratings, the car is very safe to use. The IIHS safety rating includes Side Impact Test Results (good), Moderate Overlap Front Test Results (good), Roof Strength Test Results (good), and Rear Crash Protection Results (good). Additionally, the car has a pleasant interior review. Options such as leather upholstery as well as heated front seats tend to improve the overall quality. The car has a keyless entry, 4.2-inch display, six-speaker audio system, and rear parking sensors, My Key, satellite radio, together with a rearview camera. There is also an ancillary jack for playing music and Bluetooth for making phone calls. These features make the car comfortable and entertaining to use (Kelley Blue Book Co. 2017).

The two local dealerships that sell the make and model of the car with the features include Academy Ford 13401 Baltimore Ave. Laurel MD, 20707, (877)894-4901 5300, and Eastern Automotive Group 9950 Washington Blvd N, Laurel, MD 20723 (888)493-2318


Data Collection

Year of Manufacture Age of car Price ($)
2018 0 12663
2017 1 10890
2016 2 8990
2015 3 7450
2014 4 5985
2013 5 6795
2012 6 4295
2011 7 5000
2010 8 3498
2009 9 3695
2008 10 2695
2007 11 2995


Source: Kelly Blue Book

Linear Regression Model and Graph

a) Scatter Plot


Ford Fiesta Depreciation Trend

a) Linear regression equation

The linear regression equation is


Discussion of the Regression Model

The vertical intercept is It is the mean fair purchase price value of Ford Fiesta at zero years. while the horizontal intercept is (0,13) This is the age of the car when its value will be zero. The slope is This is the rate of change of the fair purchase price with respect to the age of the car.

the predicted resale value of the car after 5 years of purchase is at $6,670. I do not expect all cars of different makes and models to have the same linear model. This is because they do not have the same MSRP. Also, some certain features may hold a better value.

It will not make sense to offer a car loan ranging up to 30 years since for most cars they will depreciate to zero before the period expires. For instance, Ford Fiesta will depreciate to zero after 13 years from the purchase date. Unlike houses, cars experience wears and tear, thus quickly losing their value.



Kelley Blue Book Co. (2017). Kelley blue book used car guide: Consumer edition, 2002-2016 models. https://www.ford.com/cars/fiesta/models/


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