3 BANKING SERVICES 3-4 Explore Compound Interest 4/26/2017 3 BANKING SERVICES 3-4 Explore Compound Interest 3-5 Compound Interest Formula 3-6 Continuous Compounding 3-7 Future Value of Investments 3-8 Present Value of Investments Chapter 1

3-4 EXPLORE COMPOUND INTEREST Banking 4/26/2017 3-4 EXPLORE COMPOUND INTEREST OBJECTIVES Understand the concept of getting interest on your interest. Compute compound interest using a table. Chapter 1

Key Terms compound interest quarterly compounding annual compounding daily compounding semiannual compounding crediting

What is compound interest? Banking 4/26/2017 What is compound interest? Define: Simple Interest Additional money earned on initial money deposited calculated once Define: Compound interest Additional money earned on initial money deposited plus all previous interest (page 137) Write down four more definitions on page 137 Annual, semiannual, quarterly, monthly Could interest be compounded every hour? How many hours are in a year? Could interest be compounded every minute? 365.25 days x 24 hours = 8766 hrs/yr. 8766 x 60 minutes = 525,960 min/yr. Chapter 1

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? I = prt I = 1000 x 0.06 x 1 I = $60.00 B = 1000 + 60 = $1060.00

CHECK YOUR UNDERSTANDING How much would x dollars earn in one year at a rate of 4.4% compounded annually?  Do Questions 2 & 3 on page 141

Example 2 Maria baldeposits $1,000 in a savings account that pays 6% interest, compounded semiannually. What is her balance after one year? I1 = p r t I1 = 1000 x 0.06 x 0.5 = 30 B1 = 1000 + 30 = $1030.00 I2 = p r t I2 = 1030 x 0.06 x 0.5 = 30.90 B2 = 1030 + 30.90 = $1060.90

CHECK YOUR UNDERSTANDING Alex deposits $4,000 in a savings account that pays 5% interest, compounded semiannually. What is his balance after one year?  Do Questions 6 on page 141

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? After one year? I1 = p r t I1 = 1000 x 0.06 x 0.25 = 15 B1 = 1000 + 15 = $1015.00 I2 = p r t I2 = 1015 x 0.06 x 0.25 = 15.23 B2 = 1015 + 15.225 = $1030.23

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 one year? I3 = p r t I3 = 1030.23 x 0.06 x 0.25 = 15.45 B3 = 1030.225 + 15.45 = $1045.68 I4 = p r t I4 = 1045.68 x 0.06 x 0.25 = 15.69 B4 = 1045.68 + 15.69 = $1061.37

CHECK YOUR UNDERSTANDING How much does $3,000 earn in six months at an interest rate of 4%, compounded quarterly?  Do Questions 7 on page 141

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.  Do Questions 8 on page 141

APPLICATIONS, page 141  Questions 2 &3 (Example 1)

Using Excel to Determine Daily Interest A = ending amount P = principal r = interest rate n = number of compoundings a year t = total number of years

Using Excel to Determine Daily Interest What is your balance after one year if you deposit $1000.00 at 6% interest (if you make no additional deposits or withdraws)? A = 1000 (1 + (0.06 / 1)) 365 * 1

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?

Example 5

Example 5

Example 5

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?

Applications, pages 141-142 Simple interest: #2 and #3 Semiannual compound interest: #6 Quarterly compound interest: #7 Daily Compound interest: #8, #10 and #11