Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 12 - Sequences and Series - 12.2 Annuities: An Application of Sequences - 12.2 Exercises - Page 621: 3

Answer

$$S = \$ 278,150.87$$

Work Step by Step

$$\eqalign{ & R = \$ 9000,\,\,\,\,\,i = 0.06,\,\,\,\,\,{\text{ and }}n = 18 \cr & {\text{The amount }}S{\text{ of an annuity of payments of }}R{\text{ dollars each}}{\text{, made at the }} \cr & {\text{ end of each period for n consecutive interest periods at a rate of interest}} \cr & {\text{ }}i{\text{ per period}}{\text{, is given b}}y \cr & S = R\left[ {\frac{{{{\left( {1 + i} \right)}^n} - 1}}{i}} \right] \cr & {\text{Substituting }}R,\,\,\,i{\text{ and }}n \cr & S = \$ 9000\left[ {\frac{{{{\left( {1 + 0.06} \right)}^{18}} - 1}}{{0.06}}} \right] \cr & {\text{Simplify by using a calculator}} \cr & S = \$ 9000\left( {30.9056} \right) \cr & S = \$ 278,150.87 \cr} $$
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