1 / 9

Section 4.1

Section 4.1. Compound Interest and Exponential Functions. If A 0 is invested at an annual interest rate r and compounded semiannually , the amount A t after t years is given by the formula. INTEREST COMPOUNDED SEMIANNUALLY.

grangerj
Download Presentation

Section 4.1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 4.1 Compound Interest and Exponential Functions

  2. If A0 is invested at an annual interest rate r and compounded semiannually, the amount At after t years is given by the formula INTEREST COMPOUNDED SEMIANNUALLY

  3. If A0 is invested at an annual interest rate r and compounded quarterly, the amount At after t years is given by the formula INTEREST COMPOUNDED QUARTERLY

  4. If A0 is invested at an annual interest rate r and compounded n times annually, the amount At after t years is given by the formula INTEREST COMPOUNEDn TIMES A YEAR

  5. THE NUMBER e The number e is an irrational number, one whose decimal expansion never terminates nor repeats. e≈ 2.718281828459045 e ≈ 2.7 1828 1828 45 90 45

  6. THE NATURAL EXPONENTIAL FUNCTION The exponential function with base e f (x) = ex is called the natural exponential function.

  7. Continuously Compounded Interest: If the initial amount A0 is invested at an annual interest rate r compounded continuously, then the resulting amount after t years is given by CONTINUOUSLY COMPOUNDED INTEREST

  8. EFFECTIVE ANNUAL YIELD Effective Annual Yield: The effective annual yield for an investment is the percentage rate that would yield the same amount of interest if the interest were compounded annually.

  9. CONTINUOUS GROWTH WITH RATE r Continuous Growth with Rate r: If the growth of a quantity is described by the function P(t) =P0ert, then we say that it grows continuously and has continuous growth rate r. The function P(t) = P0ert represents continuous grow if r is positive and continuous decay if r is negative.

More Related