chapter 8gphelps.faculty.unlv.edu/120/bztm5e_ppt_8_5.pdf · 8 solution: a. the required down...

© 2010 Pearson Prentice Hall. All rights reserved.

CHAPTER 8

Consumer Mathematics

and Financial

Management

© 2010 Pearson Prentice Hall. All rights reserved. 2

8.5

Installment Loans, Amortization, and Credit

Cards


Objectives

1. Compute the monthly payment and interest costs for

a mortgage.

2. Prepare a partial loan amortization schedule.

3. Compute payments and interest for other kinds of

installment loans.

4. Find the interest, balance due, and the minimum

monthly payment for credit card loans.


Mortgages

• A mortgage is a long-term loan for the purpose of buying a home.

• The down payment is the portion of the sale price of the home that

the buyer initially pays to the seller.

• The amount of the mortgage is the difference between the sale price

and the down payment.

• Some companies, called mortgage brokers, offer to find you a

mortgage lender willing to make you a loan.

• Fixed-rate mortgages have the same monthly payment during the

entire time of the loan.

• Variable-rate mortgages known as adjustable-rate mortgages

(ARMs), have payment amounts that change from time to time

depending on changes in the interest rate.


Computations Involved with Buying a Home

• Most lending institutions require the buyer to pay one or more

points at the time of closing—that is, the time at which the

mortgage begins.

• A point is a one-time charge that equals 1% of the loan

amount.

For example, two points means that the buyer must pay 2% of the

loan amount at closing.

• A document, called the Truth-in-Lending Disclosure

Statement, shows the buyer the APR for the mortgage.

• In addition, lending institutions can require that part of the

monthly payment be deposited into an escrow account, an

account used by the lender to pay real estate taxes and

insurance.


Loan Payment Formula for Fixed Installment Loans

The regular payment amount, PMT, required to repay a

loan of P dollars paid n times per year over t years at an

annual rate r is given by

Computation Involved with Buying a Home

.

11

nt

n

r

n

rP

PMT


The price of a home is $195,000. The bank requires a

10% down payment and two points at the time of

closing. The cost of the home is financed with a 30-year

fixed rate mortgage at 7.5%.

a. Find the required down payment.

b. Find the amount of the mortgage.

c. How much must be paid for the two points at

closing?

d. Find the monthly payment (excluding escrowed

taxes and insurance).

e. Find the total interest paid over 30 years.

Example 1: Computing the Monthly Payment

and Interest Costs for a Mortgage


Solution:

a. The required down payment is 10% of $195,000 or

0.10 $195,000 = $19,500.

b. The amount of the mortgage is the difference

between the price of the home and the down

payment.




c. To find the cost of two points on a mortgage of

$175,500, find 2% of $175,500.

0.02 $175,500 = $3510

The down payment ($19,500) is paid to the seller

and the cost of two points ($3510) is paid to the

lending institution.




d. We need to find the monthly mortgage payment for

$175,500 at 7.5% for 30 years. We use the loan

payment formula for installment loans.

The monthly mortgage payment for principal and

interest is approximately $1227.00.




e. The total cost of interest over 30 years is equal to the

difference between the total of all monthly payments

and the amount of the mortgage. The total of all

monthly payments is equal to the amount of the

monthly payment multiplied by the number of

payments. We found the amount of each monthly

payment in (d): $1227. The number of payments is

equal to the number of months in a year, 12,

multiplied by the number of years in the mortgage,

30: 12 30 = 360. Thus, the total of all monthly

payments = $1227 360.




Now we calculate the interest over 30 years.

The total interest paid over 30 years is approximately

$266,220.




Loan Amortization Schedules

• When a loan is paid off through a series of regular

payments, it is said to be amortized, which literally

means “killed off.”

• Although each payment is the same, with each

successive payment the interest portion decreases

and the principal portion increases.

• A document showing important information about the

status of the mortgage is called a loan amortization

schedule.


Prepare a loan amortization schedule for the first two

months of the mortgage loan shown in the following

table:

Example 2: Preparing a Loan Amortization

Schedule


Solution: We begin with payment number 1.

Interest for the month = Prt = $130,000 0.095 1/12 ≈ $1029.17

Principal payment = Monthly payment Interest payment

= $1357.50 $1029.17

= $328.33

Balance of loan = Principal balance Principal payment

= $130,000 $328.33

= $129,671.67


Schedule


Now, starting with a loan balance of $129,671.67, we

repeat these computations for the second month.

Interest for the month = Prt = $129,671.67 0.095 1/12 = $1026.57

Principal payment = Monthly payment – Interest payment

= $1357.50 – $1026.57

= $330.93

Balance of loan = Principal balance – Principal payment

= $129,671.67 – $330.93

= $129,340.74


Schedule



Schedule


Example 3: Comparing Car Loans

You decide to take a $20,000 loan for a new car. You

can select one of the following loans, each requiring

regular monthly payments:

Installment Loan A: 3-year loan at 7%.

Installment Loan A: 5-year loan at 9%.

a. Find the monthly payments and the total interest for

Loan A.

b. Find the monthly payments and the total interest for

Loan B.

c. Compare the monthly payments and total interest for

the two loans.


Solution:

a. We first determine monthly payments and total

interest for Loan A.

The monthly payments are approximately $618.



Now we calculate the interest paid over 3 years or 36

months.

The interest paid over 3 years is approximately $2248.



b. Next, we determine monthly payment and total

interest for Loan B.

The monthly payments are approximately $415.



Now we calculate the interest over 5 years, or 60

months.

The total interest paid over 5 years is approximately

$4900.



c. The monthly payments and total interest for the two

loans is given in the table below.


chapter 8gphelps.faculty.unlv.edu/120/bztm5e_ppt_8_5.pdf · 8 solution: a. the required down...

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