Financial Algebra 2011 Cengage Learning. All Rights Reserved. Slide CONTINUOUS COMPOUNDING Compute interest on an account that is continuously compounded. OBJECTIVES 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 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 Financial Algebra 2011 Cengage Learning. All Rights Reserved. Slide 4 Example 1 Given the quadratic function f(x) = x x + 5, as the values of x increase to infinity, what happens to the values of f(x) ? 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 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 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 Financial Algebra 2011 Cengage Learning. All Rights Reserved. Slide 8 Given the function f(x) = 2 x, find f(x). lim x EXAMPLE 3 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 Financial Algebra 2011 Cengage Learning. All Rights Reserved. Slide 10 EXAMPLE 4 If f(x) =(1 + ) x, find f(x). lim x 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., 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? 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 . Recall that = Use the e and keys on your calculator to find the difference between e and e. Round to the nearest thousandth. CHECK YOUR UNDERSTANDING 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? 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 Financial Algebra 2011 Cengage Learning. All Rights Reserved. AssignmentAssignment Pages 154 155, #2 10 even Slide 16