Slide 1

Compute interest on an account that is continuously compounded. Slide 1 OBJECTIVES

Slide 2

limit finite infinite continuous compounding exponential base (e) continuous compound interest formula Slide 2 Key Terms

Slide 3

Can interest be compounded Daily? Hourly? Each minute? Every second? If $1,000 is deposited into an account and compounded at 100% interest for one year, what would be the account balance at the end of the year? Slide 3

Slide 4

Given the quadratic function f(x) = x 2 + 3x + 5, as the values of x increase to infinity, what happens to the values of f(x)? Slide 4

Slide 5

As the values of x increase towards infinity, what happens to the values of g(x) = 5x + 1? Slide 5 CHECK YOUR UNDERSTANDING

Slide 6

Slide 6 Given the function f(x)=, as the values of x increase to infinity, what happens to the values of f(x)?

Slide 7

Slide 7 If f(x)=, use a table and your calculator to find f(x). CHECK YOUR UNDERSTANDING

Slide 8

If you deposited $1,000 at 100% interest, compounded continuously, what would your ending balance be after one year? Slide 8

Slide 9

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 . = 3.141592654 e = 2.7182818281828 Continuous Compounding formula: B = pe rt Slide 9 CHECK YOUR UNDERSTANDING

Slide 10

If you deposit $1,000 at 4.3% interest, compounded continuously, what would your ending balance be to the nearest cent after five years? Slide 10

Slide 11

Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent? Slide 11 CHECK YOUR UNDERSTANDING