Stitz-Zeager_College_Algebra_e-book

The steady state current is 2 amps 14 the linear

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Unformatted text preview: n annual rate r and 1 th compound the interest n times per year. This means the money sits in the account n of a year between compoundings. Let Ak denote the amount in the account after the k th compounding. Then r 1 A1 = P 1 + r n which simplifies to A1 = P 1 + n . After the second compounding, we use A1 r r r r2 as our new principal and get A2 = A1 1 + n = P 1 + n 1 + n = P 1 + n . Continuing in 3 4 k r r r this fashion, we get A3 = P 1 + n , A4 = P 1 + n , and so on, so that Ak = P 1 + n . Since we compound the interest n times per year, after t years, we have nt compoundings. We have just derived the general formula for compound interest below. Equation 6.2. Compounded Interest: If an initial principal P is invested at an annual rate r and the interest is compounded n times per year, the amount A in the account after t years is A(t) = P 1 + r n nt 4t 05 If we take P = 100, r = 0.05, and n = 4, Equation 6.2 becomes A = 100 1 + 0.4 which reduces 4t . This equation defines the amount A as an e...
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