4
Managing
Money
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 1
Unit 4D
Loan Payments, Credit
Cards, and Mortgages
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 2
Loan Basics

The principal is the amount of money owed at
any particular time.

An installment loan (or amortized loan) is a loan
that is paid off with equal regular payments.

The loan term is the time you have to pay back
the loan in full.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 3
Loan Payment Formula
(Installment Loans)
 APR 
P

n 

PMT 
  APR  (  nY ) 

1  1 

n 
 

PMT
P
APR
n
Y
=
=
=
=
=
regular payment amount
starting loan principal (amount borrowed)
annual percentage rate
number of payment periods per year
loan term in years
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 4
Principal and Interest for
Installment Loans
The portions of installment loan payments going
toward principal and toward interest vary as the
loan is paid down.

Early in the loan term, the portion going toward
interest is relatively high and the portion going
toward principal is relatively low.

As the term proceeds, the portion going toward
interest gradually decreases and the portion
going toward principal gradually increases.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 5
Example
Suppose you have student loans totaling
$7500 when you graduate from college.
The interest rate is APR – 9%, and the
loan term is 10 years. What are your
monthly payments? How much will you
pay over the lifetime of the loan? What is
the total interest you will pay on the
loan?
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 6
Example (cont)
Solution
We use the loan payment formula to find the
monthly payments:
 APR 
P

n 

PMT 
  APR  (  nY ) 

1  1 

n 
 

Copyright © 2015, 2011, 2008 Pearson Education, Inc.
 0.09 
$7500  

12



( 12  10 )
 

0.09 
1  1 


12 
 

Chapter 4, Unit D, Slide 7
Example (cont)
 0.09 
$7500  

12



( 12  10 )
 

0.09 
1  1 


12 
 

$7500   0.0075

1  1.0075( 120 ) 


$56.25

1  0.407937305  $95.01
Your monthly payments are $95.01. Over the
10-year term, your total payments will be
mo $95.01
10 yr  12

 $11, 401.20
yr
mo
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 8
Example (cont)
Of the $11,401.20, $7500 pays off the principal.
The rest, or $11,401 – $7500 = $3901,
represents the interest payments.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 9
Table of First Three Months
For the student loan in the previous example, the table
shows the amount of the payment that is applied to the
principal. It is easier to use software that find principal and
interest payments with built-in functions.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 10
Credit Cards
Credit cards differ from installment loans in that you
are not required to pay off your balance in any set
period of time.

A minimum monthly payment is required.

Monthly payment generally covers all the
interest but very little principal.

It takes a very long time to pay off a credit card
loan if only the minimum payments are made.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 11
Example
Suppose you have a credit card balance of $2300
with an annual interest rate of 21%. You decide to
pay off your balance over 1 year. How much will you
need to pay each month? Assume you will make no
further credit card purchases.
Solution
 APR 
 0.21 
P
$2300 
 n 
 12 



  $214.16
PMT 

  nY  
 121 
 
 
APR 
0.21 
1  1 
 1  1 



n
12


 
  

You must pay $214.16 per month to pay off the
balance in 1 year.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 12
Mortgages

A home mortgage is an installment loan
designed specifically to finance a home.

The down payment is the amount of money you
must pay up front in order to be given a
mortgage or other loan.

Closing costs are fees you must pay in order to
be given the loan. These include

direct costs, or fees charged as points, where
each point is 1% of the loan amount.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 13
Mortgages

A fixed rate mortgage is one in which the
interest rate is guaranteed not to change over the
life of the loan.

An adjustable rate mortgage is one where the
interest rate changes based on the prevailing
rates.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 14
Example
Great bank offers a $100,000, 30-year, 5% fixed
rate loan with closing costs of $500 plus 1 point. Big
Bank offers a lower rate of 4.75% on a 30-year
loan, but with Great Bank closing costs of $1000
plus 2 points. Evaluate the two options.
Solution
Great Bank
 0.05 
$100, 000  
12 

PMT 
 $536.82
1230 

 

0.5 
1  1 


12 
 

Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 15
Example (cont)
Great bank offers a $100,000, 30-year, 5% fixed
rate loan with closing costs of $500 plus 1 point. Big
Bank offers a lower rate of 4.75% on a 30-year
loan, but with closing costs of $1000 plus 2 points.
Evaluate the two options.
Big Bank:
 0.0475 
$100, 000  

12

  $521.65
PMT 
 1230  
 
0.0475 
1  1 


12 
 

Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 16
Example (cont)
You will save about $15 per month with Big Bank’s lower
interest rate. Now we must consider the difference in
closing costs. Big bank charges an extra $500 plus an
extra 1 point (1%), which is $1000 on this loan. Big Bank
cost an extra $1500 up front. We divide this to find the
time it will take to recoup this extra $1500.
$1500
1
 100 mo  8 yr
$15 / mo
2
Unless you are sure you will be staying in the house for
much more than 8 years, it is most wise to go with Big
Bank.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 17
The Relationship Between
Principal and Interest for a Payment
Portions of monthly payments going to principal and
interest over the life of a 30-year $100,000 loan at 5%
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 18
Example
You have a choice between a 30-year fixed
rate loan at 4% and an ARM with a first-year
rate of 3%. Neglecting compounding and
changes in principal, estimate your monthly
savings with the ARM during the first year on
a $100,000 loan. Suppose that the ARM rate
rises to 5% by the third year. How will your
payments be affected?
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 19
Example (cont)
Solution
Since mortgage payments are mostly interest in the
early years of a loan, we can make approximations
by assuming that the principal remains unchanged.
For the 4% fixed rate loan, the interest on the
$100,000 loan for the first year will be approximately
4% × $100,000 = $4000. With the 3% ARM, your
first-year interest will be approximately 3% ×
$100,000 = $3000. The ARM will save you about
$1000 in interest during the first year, which means
a monthly savings of about $1000 ÷ 12 ≈ $83.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 20
Example (cont)
By the third year, when rates reach 5%, the situation
is reversed. The rate on the ARM is now 1
percentage point above the rate on the fixed rate
loan. Instead of saving $83 per month, you’d be
paying $83 per month more on the ARM than on the
4% fixed rate loan. Moreover, if interest rates remain
high on the ARM, you will continue to make these
high payments for many years to come. Therefore,
while ARMs reduce risk for the lender, they add risk
for the borrower.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Chapter 4, Unit D, Slide 21