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Unformatted text preview: draw your money and try to invest it at the higher rate there. Since six months
is one half of a year, that initial $100 yields $100(0.05) 1 = $2.50 in interest. You take your
$102.50 oﬀ to the competitor and ﬁnd out that those restrictions which may apply actually do
apply to you, and you return to your bank which happily accepts your $102.50 for the remaining
six months of the year. To your surprise and delight, at the end of the year your statement reads
$105.06, not $105 as you had expected.3 Where did those extra six cents come from? For the ﬁrst
six months of the year, interest was earned on the original principal of $100, but for the second
six months, interest was earned on $102.50, that is, you earned interest on your interest. This is
the basic concept behind compound interest. In the previous discussion, we would say that the
interest was compounded twice, or semiannually.4 If more money can be earned by earning interest
on interest already earned, a natural question to ask is what happens if the interest is com...
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