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Page 1: Section 3.4 Explore Compound Interest (blank) Section 3.4 Explore Compound... · Financial Algebra Chapter 3: Banking Services Section 3.4 1

Financial Algebra

Chapter 3: Banking Services

Section 3.4 1

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Section 3.4:

EXPLORE COMPOUND INTEREST

Understand the concept of getting

interest on your interest.

Compute compound interest using a

table.

OBJECTIVES

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

� compound interest

� annual compounding

� semiannual compounding

� quarterly compounding

� daily compounding

� crediting

Key Terms

Page 2: Section 3.4 Explore Compound Interest (blank) Section 3.4 Explore Compound... · Financial Algebra Chapter 3: Banking Services Section 3.4 1

Financial Algebra

Chapter 3: Banking Services

Section 3.4 2

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Who will make more money?Who will make more money?

Investor A

Opens a Retirement

Account

at age 26 and deposits $2,000 at

average growth rate of 10%. The investor continues to make deposits

until age 65.

Investor A

Opens a Retirement

Account

at age 26 and deposits $2,000 at

average growth rate of 10%. The investor continues to make deposits

until age 65.

Investor B

Opens a Retirement

Account

at age 19 and deposits $2,000 at

average growth rate of 10%. After 7 years, makes no

more deposits.

Investor B

Opens a Retirement

Account

at age 19 and deposits $2,000 at

average growth rate of 10%. After 7 years, makes no

more deposits.

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Who will make more money?Who will make more money?

Answer

WHY?

Page 3: Section 3.4 Explore Compound Interest (blank) Section 3.4 Explore Compound... · Financial Algebra Chapter 3: Banking Services Section 3.4 1

Financial Algebra

Chapter 3: Banking Services

Section 3.4 3

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

1. Compound interestis the interest earned on the money deposited plus previous interest.

This is not how simple interest accounts work.

Recall: only the original principal is used to

calculate simple interest.

Compound InterestCompound Interest

Compound Interest

Calculator

How does compounding interest work?How does compounding interest work?

Page 4: Section 3.4 Explore Compound Interest (blank) Section 3.4 Explore Compound... · Financial Algebra Chapter 3: Banking Services Section 3.4 1

Financial Algebra

Chapter 3: Banking Services

Section 3.4 4

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Types of Compounding InterestTypes of Compounding Interest

Annual Compounding

• Interest compounded once per year

• Same as simple interest

Semiannual Compounding

• Interest compounded twice per year, or every six months

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Types of Compounding InterestTypes of Compounding Interest

Quarterly Compounding

• Interest compounded four times per year, or every three months

Daily Compounding

• Interest compounded every day

• There are 365 days in a year and 366 days in a leap year

Page 5: Section 3.4 Explore Compound Interest (blank) Section 3.4 Explore Compound... · Financial Algebra Chapter 3: Banking Services Section 3.4 1

Financial Algebra

Chapter 3: Banking Services

Section 3.4 5

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Types of Compounding InterestTypes of Compounding Interest

What is the most common form of compounding?

Daily Compounding

Banks pay interest every day based on that day’s principal.

Banks keep a record of the interest and add it to the account monthly or quarterly which is called crediting an account.

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Example 1

How much interest would $1,000 earn in one year at a rate of 6%,

compounded annually? What would be the new balance?

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Financial Algebra

Chapter 3: Banking Services

Section 3.4 6

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Example 2

Maria deposits $1,500 in a savings account that pays 5.5% interest,

compounded semiannually.

(a) How much interest does Maria earn after six months?

(b) What is the balance after six months?

(c) How much interest does Maria earn over the next six months?

(d) What is her balance after one year?

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Alex deposits $4,000 in a savings account that pays 5% interest,

compounded semiannually. What is his balance after one year?

Example 3

Example 4

How much interest does $2,000 earn in three months at an interest

rate of 4.25%, compounded quarterly?

What is the balance after three months?

Page 7: Section 3.4 Explore Compound Interest (blank) Section 3.4 Explore Compound... · Financial Algebra Chapter 3: Banking Services Section 3.4 1

Financial Algebra

Chapter 3: Banking Services

Section 3.4 7

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

How much does $3,000 earn in six months at a 4% interest rate,

compounded quarterly?

Example 5

Example 6

How much interest does $1,200 earn in one day at an interest rate

of 3.5%, compounded daily? What is the balance after a day?

Financial Algebra

© 2011 Cengage Learning. All Rights Reserved.

Erin has a bank account that

compounds interest daily at a rate

of 3.2%. On July 11, the principal

is $1,234.98. She withdraws $200

for a car repair. She receives a $34

check from her health insurance

company and deposits it. On July

12, she deposits her $345.77

paycheck. What is her balance at

the end of the day on July 12?

Example 7 Creating a table is helpful ☺☺☺☺