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Stitz-Zeager_College_Algebra_e-book

# 54 395 answers 1 a a8 2000 1 00025 128 12 204040 ln2

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Unformatted text preview: pounded more often, say 4 times a year, which is every three months, or ‘quarterly.’ In this case, the money is in the account for three months, or 1 of a year, at a time. After the ﬁrst quarter, we 4 1 How generous of them! Some restrictions may apply. 3 Actually, the ﬁnal balance should be \$105.0625. 4 Using this convention, simple interest after one year is the same as compounding the interest only once. 2 6.5 Applications of Exponential and Logarithmic Functions 379 have A = P (1 + rt) = \$100 1 + 0.05 · 1 = \$101.25. We now invest the \$101.25 for the next three 4 months and ﬁnd that at the end of the second quarter, we have A = \$101.25 1 + 0.05 · 1 ≈ \$102.51. 4 Continuing in this manner, the balance at the end of the third quarter is \$103.79, and, at last, we obtain \$105.08. The extra two cents hardly seems worth it, but we see that we do in fact get more money the more often we compound. In order to develop a formula for this phenomenon, we need to do some abstract calculations. Suppose we wish to invest our principal P at a...
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