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Math 1730

Project

1

K.

Pueringer

Financing a Purchase

At some point in your life, you are likely to need to borrow money to finance a purchase. For example,

most of us will finance the purchase of a car or a home. What is the mathematics behind financing a

purchase? When you

borrow money from a bank, the bank uses a rather complex equation (or formula)

to determine how much you need to pay each month to repay the loan. There are a number of variables

that determine the monthly payment. These variable

s

include the amount borr

owed, the interest rate, and

the length of the loan. The interest rate is based on current economic conditions, the length of the loan,

the type of item being purchased, and your credit history.

The following formula gives the monthly payment

require

d to pay off a loan amount

at an annual

interest rate

, expressed as a decimal, but usually given as a percent. The time

, measured in months, is

the length of the loan. For example, a 30

-

year loan requires 12 X 30=360 monthly payments.

Use this

f

ormula to complete this project.

=

[

12

1

(

1

+

12

)

t

]

1.

Interest rates change daily. Many websites post current interest rates on loans.

Go to

www.bankrate.com

and find the current best interest rate on a 60

-

month new

-

car purchase loan.

Across the top of the of the webpage, choose

"

Loans

"

and then

"

Auto Loans

"

. Change your

search to only show

60

-

month new car loans. Choose the

best

i.e. lowest interest rate.

Sometimes bankrate.com will only show one rate or list the interest rate as 0% which is not

interesting and defeats the purpose of the proje

ct. If this is the case,

I recommend using

www.interest.com

and choosing 'Cars' and 'Car Loans'.

You will have to choose a city and

sometimes St. Paul is not

listed so choose whichever city is closest to you.

Remember, choose

the best interest rate for the particular loan you are working with.

Math 1730

Project

1

K.

Pueringer

a.

Use

the best

rate to determine the monthly payment on a $30,000 automobile loan.

o

Round your payment to the nearest cent.

Use the formula above and sho

w your work.

Do not use an online payment calculator.

o

State which lender has the best interest rate and the date you pulled the data.

b.

Determine the total amount paid for the loan by multiplying the loan payment by the term of

the loan.

o

For example,

if you calculated your monthly payment to be $350.13 and the term of your

loan was 30 months, the total amount you would pay for the loan would be $350.13 per

month X 30 months = $10,503.90

c.

Determine the total amount of interest paid by subtracting the

loan amount paid from part b

.

o

For example, if the loan amount was $20,000 and your answer from question 2 was

$23,000, the total interest paid would be $23,000

-

$20,000=$3,000.

d.

More often than not, we decide how much of a payment we can afford and use tha

t

information to determine the loan amount.

i.

Suppose you can afford a monthly payment of $500. Use the interest rate from

part a

to

determine the maximum amount you can borrow. In other words, if you know

,

, and

, solve for

.

ii.

If you have $5,000 to put down on the car,

how does this change your monthly payment

from part i

?

What will your new monthly payment be?

In other words, subtract $5000

from the value of L found in part (i) and recalculate the monthly payment.

2.

Repeat que

stion 1

a

-

d

using a

different

new

-

car purchase loan

with a

different

term

than the

loan from

part a

.

Keep the principal, $30,000, the same.

o

List the term of

the

loan.

o

State the lender, interest rate,

and the date you pulled the data.

o

R

ound your

answers

to the nearest cent.

3.

Repeat question 1

a

-

d

using a

used

-

car purchase loan

with a

different

term

than the loans from

problems 1 and 2. Keep the principal, $30,000, the same.

o

List the term of

the

loan.

o

State the lender, interest rate,

and the date you pulled the data.

o

R

ound your

answers

to the nearest cent.

4.

Based on your calculations from #1

-

3, which type of loan would you use to purchase a car?

Justify your reasoning.

Decide on a

specific

vehicle you would purchase

using your chose

n loan

type.

Go to an online automobile website such as

www.cars.com

,

www.edmunds.com

, or

www.autobytel.com

.

Use your chosen loan type to

determine your monthly payment for your

chosen car.

Math 1730

Project

1

K.

Pueringer

Project Submission Directions

Complete this project on separate paper. In other words, do not print this paper and write answers

in the margins.

Submit s

cratchwork but do not type it

. Take a pho

to and upload it or turn it into my mailbox.

Express all answers using complete sentences.

Submit via the D2L

Assignments folder

titled "Project 1"

OR place your project in my mailbox

(#132

)

on campus by the due date

.

Late su

bmissions will be accepted up t

o

7

days

past the due date and will be docked points. Late

submissions should be submitted in the D2L

Assignments folder

titled "Project 1 Late

Submissions"