1. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 3-6 CONTINUOUS COMPOUNDING Compute interest on an account that is continuously compounded. OBJECTIVES

2. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Warm-UpWarm-Up Determine the exact value of each. 1. when A = 8 2.A bc when A = 9, b = 2, c = (1/4) Slide 2

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 limit - restriction finite – represented by a real number infinite - unlimited continuous compounding – compounding infinitely many times a year exponential base ( e ) - continuous compound interest formula – B = pe rt Key Terms

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 4 Example 1 Given the quadratic function f(x) = x 2 + 3 x + 5, as the values of x increase to infinity, what happens to the values of f(x) ?

5. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 As the values of x increase towards infinity, what happens to the values of g(x) = –5 x + 1? CHECK YOUR UNDERSTANDING

6. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6 Given the function f(x)=, as the values of x increase to infinity, what happens to the values of f(x)? Example 2

7. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 If f(x)=, use a table and your calculator to find f(x). CHECK YOUR UNDERSTANDING

8. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 8 Given the function f(x) = 2 x, find f(x). lim x  EXAMPLE 3

9. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 9 CHECK YOUR UNDERSTANDING Given the function f(x) = 1 x, find f(x). lim x 

10. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 EXAMPLE 4 If f(x) =(1 + ) x, find f(x). lim x 

11. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 CHECK YOUR UNDERSTANDING Use a table and your calculator to find rounded to five decimal places.,

12. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 12 EXAMPLE 5 If you deposited $1,000 at 100% interest, compounded continuously, what would your ending balance be after one year?

13. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 13 The irrational, exponential base e is so important in mathematics that it has a single-letter abbreviation, e, and has its own key on the calculator. When you studied circles, you studied another important irrational number that has a single-letter designation and its own key on the calculator. The number was π. Recall that π = 3.141592654. Use the e and π keys on your calculator to find the difference between e π and π e. Round to the nearest thousandth. CHECK YOUR UNDERSTANDING

14. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 14 EXAMPLE 6 If you deposit $1,000 at 4.3% interest, compounded continuously, what would your ending balance be to the nearest cent after five years?

15. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 15 Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent? CHECK YOUR UNDERSTANDING

16. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. AssignmentAssignment Pages 154 – 155, #2 – 10 even Slide 16