Section 3.4: EXPLORE COMPOUND INTEREST. Understand the concept of getting interest on your interest. Compute compound interest using a table.

Transcription

1 Section 3.4: EXPLORE COMPOUND INTEREST OBJECTIVES Understand the concept of getting interest on your interest. Compute compound interest using a table. Key Terms compound interest annual compounding semiannual compounding quarterly compounding daily compounding crediting Section 3.4 1

2 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 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. Who will make more money? Answer WHY? Section 3.4 2

3 Compound Interest 1. Compound interest is the interest earned on the money deposited plus previous interest. This is nothow simple interest accounts work. Recall: only the original principalis used to calculate simple interest. Compound Interest Calculator How does compounding interest work? Section 3.4 3

4 Types 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 Types 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 Section 3.4 4

5 Types 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 creditingan account. 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? Section 3.4 5

6 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? Example 3 Alex deposits $4,000 in a savings account that pays 5% interest, compounded semiannually. What is his balance after one year? 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? Section 3.4 6

7 Example 5 How much does $3,000 earn in six months at a 4% interest rate, compounded quarterly? 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? Example 7 Erin has a bank account that compounds interest daily at a rate of 3.2%. On July 11, the principal is $1, 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 $ paycheck. What is her balance at the end of the day on July 12? Creating a table is helpful Section 3.4 7