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Stitz-Zeager_College_Algebra_e-book

# Do you see why not the reader is encouraged to think

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Unformatted text preview: the number of compoundings per year to inﬁnity results in what is called continuously compounded interest. Theorem 6.8. If you invest \$1 at 100% interest compounded continuously, then you will have \$e at the end of one year. 6 In fact, the rate of increase of the amount in the account is exponential as well. This is the quality that really deﬁnes exponential functions and we refer the reader to a course in Calculus. 7 Once you’ve had a semester of Calculus, you’ll be able to fully appreciate this very lame pun. 8 Or deﬁne, depending on your point of view. 6.5 Applications of Exponential and Logarithmic Functions 381 Using this deﬁnition of e and a little Calculus, we can take Equation 6.2 and produce a formula for continuously compounded interest. Equation 6.3. Continuously Compounded Interest: If an initial principal P is invested at an annual rate r and the interest is compounded continuously, the amount A in the account after t years is A(t) = P ert If we take the scenario of Example 6.5.1 and compare monthly compounding to continuous compound...
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