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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
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?
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?
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
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?
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?
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 ☺☺☺☺