Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 11

3-6

CONTINUOUS COMPOUNDING

Compute interest on an account that is continuously compounded.

OBJECTIVES

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 22

limit finite infinite continuous compounding exponential base (e)

e 2.718281828

continuous compound interest formulaB = pert

Key Terms

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 33

Given the quadratic function f(x) = x2 + 3x + 5, as the values of x increase to infinity, what happens to the values of f(x)?

x f(x)

1001,000

90,000900,000

8,000,00050,000,000

EXAMPLE 1EXAMPLE 1

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 44

EXAMPLE 2EXAMPLE 2

If f(x) =(1 + )x, find f(x).limx

1

x

x f(x)

1001,000

90,000900,000

8,000,00050,000,000

2,000,000,000

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 55

EXAMPLE 3EXAMPLE 3

If you deposited $1,000 at 100% interest, compounded continuously, what would your ending balance be to the nearest cent after one year?

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 66

EXAMPLE 4EXAMPLE 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?

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 77

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

EXAMPLE 5EXAMPLE 5