Compound Interest and

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Section 4.1

• Compound Interest and
• Exponential Functions

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INTEREST COMPOUNDED SEMIANNUALLY
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INTEREST COMPOUNDED QUARTERLY
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INTEREST COMPOUNEDn TIMES A YEAR
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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
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THE NATURAL EXPONENTIAL FUNCTION
The exponential function with base e f (x)
ex is called the natural exponential function.
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CONTINUOUSLY COMPOUNDED INTEREST
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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.
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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.