Explore Compound Interest 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: How much would you have at the end of 20 days? How does this problem relate to the concept of compound interest? 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