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. Slide 2 limit finite infinite continuous compounding exponential base ( e ) e  2.718281828 continuous compound interest formula B = pe rt Key Terms

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 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) ? xf(x) 100 1,000 90,000 900,000 8,000,000 50,000,000 EXAMPLE 1

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 4 EXAMPLE 2 If f(x) =(1 + ) x, find f(x). lim x  xf(x) 100 1,000 90,000 900,000 8,000,000 50,000,000 2,000,000,000

5. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 EXAMPLE 3 If you deposited $1,000 at 100% interest, compounded continuously, what would your ending balance be to the nearest cent after one year?

6. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6 EXAMPLE 4 If you deposit $1,000 at 4.3% interest, compounded continuously, what would your ending balance be to the nearest cent after five years?

7. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent? EXAMPLE 5