SECTION 3.4
Explore Compound Interest
WHAT IS COMPOUND INTEREST?
Compound interest is the concept that when interest is added to
principal, the principal increases, and the resulting interest for the next
period increases.
COMPOUND INTEREST ACTIVITY
What would happen if you received
1 penny ($0.01), the next day you received
2 pennies, the next day you received
4 pennies, and so on for a total of 20 days.
In your groups, answer the following questions:
1) How much would you have at the end of 20 days?
2) How does this problem relate to the concept of compound
interest?
3) What would the daily interest rate be?
When opening a bank account, consumers should be aware of both the annual
interest rate and how the interested is calculated.
compound interest – interest that is earned on the money deposited into an
account plus previous interest
Remember that for simple interest, only the original principal is used to compute
annual interest.
HOW OFTEN IS INTEREST COMPOUNDED?
annual compounding – interest is compounded once
each year
semiannual compounding – interest is compounded twice
per year, or every 6 months
quarterly compounding – interest is compounded four
times per year, or every 3 months
daily compounding – interest is compounded every
day; there are 365 days in a year, 366 days in a leap
year, so an average of 365.25 days in a year
The most common form of compounding is daily compounding.
crediting – interest that is compounded daily but added to the account later
Most banks today compound interest daily and credit monthly.
Lets look at some different accounts and how interest is compounded.
http://www.bankrate.com/
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?
CHECK YOUR UNDERSTANDING
How much would x dollars earn in one year at a rate of 4.4%
compounded annually?
EXAMPLE 2
Maria deposits $1,000 in a savings account that pays 6% interest,
compounded semiannually. What is her balance after one year?
CHECK YOUR UNDERSTANDING
Alex deposits $4,000 in a savings account that pays 5% interest,
compounded semiannually. What is his balance after one year?
EXAMPLE 3
How much interest does $1,000 earn in three months at an interest
rate of 6%, compounded quarterly? What is the balance after three
months?
CHECK YOUR UNDERSTANDING
How much does $3,000 earn in six months at an interest rate of 4%,
compounded quarterly?
EXAMPLE 4
How much interest does $1,000 earn in one day at an interest rate of
6%, compounded daily? What is the balance after a day?
CHECK YOUR UNDERSTANDING
How much interest does x dollars earn in one day at an interest rate
of 5%, compounded daily? Express the answer algebraically.
EXAMPLE 5
Jennifer 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?
CHECK YOUR UNDERSTANDING
On January 7, Joelle opened a savings account with $900. It earned
3% interest, compounded daily. On January 8, she deposited her first
paycheck of $76.22. What was her balance at the end of the day on
January 8?
3.4 HW
p.141#2-4all; 6-11all