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Section 8.6Amortization and the Cost of Home Ownership

Objectives

1. Understand mortgage options.2. Compute the monthly payment and interest costs for a

mortgage.3. Prepare a partial loan amortization schedule.4. Compute payments and interest for other kinds of

installment 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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Computation 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 onetime 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 Installment Loans

The regular payment amount, PMT, required to repay a loan of P dollars paid n times per years over t years at an annual rate r is given by

Computation Involved with Buying a Home

.11

nt

nrnrP

PMT

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Example: 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.

Computation Involved with Buying a Home

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

0.10 x $195,000 = $19,500.b. The amount of the mortgage is the difference between

the price of the home and the down payment.

Computation Involved with Buying a HomeExample Continued

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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 x $175,000 = $3510

The down payment ($19,500) is paid to the seller and the cost of two points ($3510) is paid to the lending institution.

Computation Involved with Buying a HomeExample Continued

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d. We need to find the monthly mortgage payment for $175,000 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.

Computation Involved with Buying a HomeExample Continued

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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 x 30 = 360. Thus, the total of all monthly payments = $1227 x 360.

Computation Involved with Buying a HomeExample Continued

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Now we calculate the interest over 30 years.

The total interest paid over 30 years is approximately $266,220.

Computation Involved with Buying a HomeExample Continued

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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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Example: Prepare a loan amortization schedule for the first two months of the mortgage loan shown in the following table:

Loan Amortization Schedules

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Solution: We begin with payment number 1.

Interest for the month = Prt = $130,000 x 0.095 x ≈ $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

Loan Amortization SchedulesExample Continued

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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 x 0.095 x = $1026.57

Principal payment = Monthly payment – Interest payment = $1357.50 – $1026.57 = $330.93Balance of loan = Principal balance – Principal payment = $129,671.67 – $330.93 = $129,340.74

Loan Amortization SchedulesExample Continued

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Loan Amortization SchedulesExample Continued

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Monthly Payments and Interest Costs for Other Kinds of Installment Loans

Example: 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.

Monthly Payments and Interest Costs for Other Kinds of Installment 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.

Monthly Payments and Interest Costs for Other Kinds of Installment Loans

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b. Next, we determine monthly payment and total interest for Loan B.

The monthly payments are approximately $415.

Monthly Payments and Interest Costs for Other Kinds of Installment 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.

Monthly Payments and Interest Costs for Other Kinds of Installment Loans

Assignment - 14Section 8.6 21

c. The monthly payments and total interest for the two loans is given in the table below.

Monthly Payments and Interest Costs for Other Kinds of Installment Loans