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CHAPTER 8
Consumer Mathematics
and Financial
Management
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8.5
Installment Loans, Amortization, and Credit
Cards
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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.
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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.
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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.
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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
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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
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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.
Example 1: Computing the Monthly Payment
and Interest Costs for a Mortgage
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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.
Example 1: Computing the Monthly Payment
and Interest Costs for a Mortgage
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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.
Example 1: Computing the Monthly Payment
and Interest Costs for a Mortgage
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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.
Example 1: Computing the Monthly Payment
and Interest Costs for a Mortgage
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Now we calculate the interest over 30 years.
The total interest paid over 30 years is approximately
$266,220.
Example 1: Computing the Monthly Payment
and Interest Costs for a Mortgage
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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.
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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
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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
Example 2: Preparing a Loan Amortization
Schedule
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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
Example 2: Preparing a Loan Amortization
Schedule
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Example 2: Preparing a Loan Amortization
Schedule
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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.
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Solution:
a. We first determine monthly payments and total
interest for Loan A.
The monthly payments are approximately $618.
Example 3: Comparing Car Loans
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Now we calculate the interest paid over 3 years or 36
months.
The interest paid over 3 years is approximately $2248.
Example 3: Comparing Car Loans
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b. Next, we determine monthly payment and total
interest for Loan B.
The monthly payments are approximately $415.
Example 3: Comparing Car Loans
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Now we calculate the interest over 5 years, or 60
months.
The total interest paid over 5 years is approximately
$4900.
Example 3: Comparing Car Loans
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c. The monthly payments and total interest for the two
loans is given in the table below.
Example 3: Comparing Car Loans