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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
1 How generous of them!
Some restrictions may apply.
Actually, the ﬁnal balance should be $105.0625.
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
months and ﬁnd that at the end of the second quarter, we have A = $101.25 1 + 0.05 · 1 ≈ $102.51.
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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