Unlike most of the phenomena we have studied in this

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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 2 $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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