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<font size="4" style="font-family: times new roman,times,serif; font-style: italic;"><span class="notranslate"><span class="a" style="left: 712px; top: 4566px; word-spacing: 3px;">Cierto capital de <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«/math»</span> UF será invertido durante <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#b«/mi»«/math»</span> meses al: <br />a) <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#i«/mi»«mo»%«/mo»«/math»</span> de <span style="font-weight: bold;">interés simple</span>, generando </span></span></font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;">{1:SA:=\#sol1#¡Muy bien! Sigue así!} </font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"><span class="notranslate"><span class="a" style="left: 712px; top: 4566px; word-spacing: 3px;">UF de interés, <br />b) <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#j«/mi»«mo»%«/mo»«/math»</span> de <span style="font-weight: bold;">interés compuesto</span> generando</span></span></font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"> {1:SA:=\#sol4#¡Muy bien! Sigue así!}</font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"><span class="notranslate"><span class="a" style="left: 712px; top: 4566px; word-spacing: 3px;"> UF de interés.<br /><br /></span></span></font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"><span class="notranslate"><span class="a" style="left: 712px; top: 4566px; word-spacing: 3px;"></span></span></font><font size="4" style="font-family: times new roman,times,serif;"><span style="color: rgb(153, 0, 0); font-style: italic;">Obs.:</span><span style="color: rgb(153, 0, 0); font-style: italic; font-weight: bold;"> <br /></span></font> <br style="color: rgb(153, 0, 0); font-family: times new roman,times,serif; font-style: italic;" /><font size="4" style="color: rgb(153, 0, 0); font-family: times new roman,times,serif; font-style: italic;">1. Si el resultado es decimal, recuerda aproximar a la centésima.</font><br style="color: rgb(153, 0, 0); font-family: times new roman,times,serif; font-style: italic;" /><font size="4"><span style="color: rgb(153, 0, 0); font-family: times new roman,times,serif; font-style: italic;">2. Para separar los decimales escribe un punto en vez de una coma.</span><br /></font> <ol style="font-family: times new roman,times,serif;"> </ol><br /> <p> </p>
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<font size="4"> <font size="4" style="font-family: times new roman,times,serif; font-style: italic;">Solución<br /></font></font><span style="font-family: times new roman,times,serif; font-style: italic;"><font size="4">a) Recordemos la fórmula para el interés simple</font>: </span><span style="font-family: times new roman,times,serif;"><font size="5">I= C</font></span><font size="5"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»·«/mo»«/math»</span><span style="font-family: times new roman,times,serif;">i</span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»·«/mo»«/math»</span><span style="font-family: times new roman,times,serif;">t</span></font><br /><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"> </font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;">Debemos calcular el interés que genera cierto capital "C" en "t" años, al "i" % de interés simple. <br /><br />Nuestros datos son: <br /><br />C<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#a«/mi»«/math»</span>UF<br />i<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#i«/mi»«mo»%«/mo»«/math»</span>=, es decir, i<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#i1«/mi»«/math»</span><br />n<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#b«/mi»«/math»</span> meses, es decir, <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#b2«/mi»«/math»</span> años<br /><br />Reemplazando nuestros datos en la fórmula, obtenemos:<br /><br /> </font><font size="4"><span style="font-family: times new roman,times,serif;"> I= C</span></font><font size="4"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»·«/mo»«/math»</span><span style="font-family: times new roman,times,serif;">i</span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»·«/mo»«/math»</span><span style="font-family: times new roman,times,serif;">t</span> <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»§#8658;«/mo»«/math»</span><span style="font-family: times new roman,times,serif;"> I<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#a«/mi»«mo»·«/mo»«mi»#i1«/mi»«mo»·«/mo»«mi»#b2«/mi»«/math»</span></span><span style="font-family: times new roman,times,serif;"></span><span style="font-family: times new roman,times,serif;"></span></font><br /><font size="4"><span style="font-family: times new roman,times,serif;"> I<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#sol1«/mi»«/math»</span></span></font><br /><span style="font-family: times new roman,times,serif;"><font size="4"><span style="font-style: italic;"><br />Es decir, el interés generado será de</span></font><span style="font-style: italic;"> <font size="4"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#sol1«/mi»«/math»</span> </font></span><font size="4"><span style="font-family: times new roman,times,serif; font-style: italic;">UF.</span></font></span><br /><br style="font-family: times new roman,times,serif;" /><span style="font-family: times new roman,times,serif; font-style: italic;"><font size="4">b)Recordemos la fórmula para el interés compuesto</font>:<font size="4"> </font></span><font size="4"><span style="font-family: times new roman,times,serif;">M= C</span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»·«/mo»«/math»</span><span style="font-family: times new roman,times,serif;">(1+i)<sup>n</sup></span></font> ,<span style="font-family: times new roman,times,serif; font-style: italic;"><font size="4">donde</font> "<font size="4">M</font> " <font size="4">corresponde al monto o capital final. </font><font size="4">El interés se calcula</font></span> <font size="4"><span style="font-family: times new roman,times,serif;">I=M-C</span></font>, <font size="4" style="font-style: italic;"><span style="font-family: times new roman,times,serif;">es decir, capital final menos el capital inicial</span></font>.<br /><br /><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"> </font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;">Debemos calcular el interés que genera cierto capital "C" en "n" años, al "i" % de interés compuesto. <br /><br />Nuestros datos son: <br /><br />C<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#a«/mi»«/math»</span> UF<br />i<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#j«/mi»«mo»%«/mo»«/math»</span>, es decir, i<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#j1«/mi»«/math»</span><br />n<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#b«/mi»«/math»</span> meses, es decir, <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#b2«/mi»«/math»</span> años<br /><br />Reemplazando nuestros datos en la fórmula, obtenemos:<br /><br /></font><span style="font-family: times new roman,times,serif; font-style: italic;"> </span><font size="4"><span style="font-family: times new roman,times,serif;">M= C</span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»·«/mo»«/math»</span><span style="font-family: times new roman,times,serif;">(1+i)<sup>n</sup></span><span style="font-family: times new roman,times,serif;"></span></font> <font size="4"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»§#8658;«/mo»«/math»</span><span style="font-family: times new roman,times,serif;"> <font size="4">C<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#a«/mi»«mo»·«/mo»«msup»«mfenced»«mrow»«mn»1«/mn»«mo»+«/mo»«mi»#j1«/mi»«/mrow»«/mfenced»«mrow»«mi»#b2«/mi»«/mrow»«/msup»«/math»</span></font></span><font size="4"><span style="font-family: times new roman,times,serif;"></span></font></font><br /><br /><font size="4"><span style="font-family: times new roman,times,serif;">M<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#sol3«/mi»«/math»</span></span></font>,<span style="font-family: times new roman,times,serif; font-style: italic;"> <font size="4" style="font-style: italic;">luego el interés correponderá a</font></span><font size="4"><span style="font-style: italic;"> </span></font><font size="4"><span style="font-family: times new roman,times,serif;">I=M-C</span></font><br /><font size="4"><span style="font-family: times new roman,times,serif;"> I<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#sol3«/mi»«mo»-«/mo»«mi»#a«/mi»«/math»</span> </span></font><font size="4"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»§#8658;«/mo»«/math»</span></font><font size="4"><span style="font-family: times new roman,times,serif;"> I<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#sol4«/mi»«/math»</span></span></font>.<br /><span style="font-family: times new roman,times,serif;"><font size="4" style="font-style: italic;">En consecuencia, el interés generado será de <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#sol4«/mi»«/math»</span> <span style="font-family: times new roman,times,serif;">UF.</span></font></span><br /><br style="font-family: times new roman,times,serif; font-style: italic;" />
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