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5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} </style> <![endif]--> <p class="MsoList2" style="line-height: 200%; text-indent: 0cm; font-family: times new roman,times,serif; margin-left: 0cm;"><font size="4"><span class="a" style="font-style: italic;"><span lang="ES" style="padding: 0cm; border: 1pt windowtext; color: black; line-height: 200%; font-size: 14pt; background-image: none; background-attachment: scroll; background-repeat: repeat; background-size: auto auto; background-origin: padding-box; background-clip: border-box;">Si una empresa deposita <span class="nolink">«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»#a«/mi»«/math»</span> UF a una tasa de </span><span style="word-spacing: 11px; orphans: 2; widows: 2;">interés compuesto anual del #i% capitalizable</span><span style="word-spacing: 13px; orphans: 2; widows: 2;"> #m, el monto acumulado </span><span style="word-spacing: -1px; orphans: 2; widows: 2;">en #t años será de</span></span><span style="font-style: italic;"> {1:SA:=\#sol1#¡Excelente!} UF</span></font><span style="font-style: italic;">.</span><br /></p><br /> <p> </p>
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<font size="4" style="font-family: wingdings; font-style: italic;"> <font size="4" style="font-family: times new roman,times,serif;">Solución<br /><br style="font-weight: bold;" /></font></font><font size="4" style="font-family: wingdings; font-style: italic;"><span style="font-weight: bold;"> </span></font><font size="4" style="font-family: wingdings; font-style: italic;"><span style="font-weight: bold;"></span></font><span style="font-family: wingdings; font-style: italic;"><font size="4">La fórmula para el interés compuesto es</font> : <span style="font-weight: bold;">M=C ( 1+ i )</span></span><sup style="font-family: wingdings; font-style: italic; font-weight: bold;">n</sup><font size="4" style="font-family: wingdings; font-style: italic;"> donde:<br /><br />M : es el monto que se obtendrá.<br />C : es el capital que será invertido.<br />n : es el tiempo en años.<br />i : es el porcentaje o tasa de interés dada para la inversión.<br /><br />Importante señalar que si la tasa es "capitalizable", se refiere al rendimiento en "cierto período" de tiempo dentro de un año. Esto es:<br /><br /> <table style="width: 660px; height: 91px;" border="1"><tbody> <tr> <td width="20%" valign="top">1 año <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»§#8658;«/mo»«/math»</span><br /> </td> <td width="20%" valign="top">mensualmente<br /> </td> <td width="20%" valign="top">bimensualmente<br /> </td> <td width="20%" valign="top">trimestralmente<br /> </td> <td width="20%" valign="top">semestralmente<br /> </td> </tr> <tr> <td width="20%" valign="top">rinde en un año<br /> </td> <td width="20%" valign="top"> 12 veces<br /> </td> <td width="20%" valign="top"> 6 veces<br /> </td> <td width="20%" valign="top"> 4 veces<br /> </td> <td width="20%" valign="top"> 2 veces<br /> </td> </tr></tbody> </table><br />Es decir, la tasa i= #i % <span style="font-weight: bold;">capitalizable</span> #m debe usarse como i dividido por el rendimiento que tiene en un año. En este caso #p veces.<br />Luego la tasa será <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mfrac»«mrow»«mi»#i1«/mi»«/mrow»«mrow»«mi»#p«/mi»«/mrow»«/mfrac»«/math»</span><br />El tiempo también debe considerar estos períodos, por tanto, la cantidad de años debe multiplicarse por dichos períodos que posee en un año.<br /></font><font size="4" style="font-family: wingdings; font-style: italic;"><br />En nuestro caso "n" será </font><font size="4" style="font-family: wingdings; font-style: italic;"> <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#t«/mi»«/math»</span>años multiplicado por <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#p«/mi»«/math»</span> períodos.<br /><font size="4">n=</font></font><font size="4" style="font-family: wingdings; font-style: italic;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#t«/mi»«/math»</span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»·«/mo»«/math»</span></font><font size="4" style="font-family: wingdings; font-style: italic;"><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#p«/mi»«/math»</span></font><span style="font-family: wingdings; font-style: italic;"><font size="4"> luego n</font>=</span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#n«/mi»«/math»</span><br style="font-family: wingdings; font-style: italic;" /><span style="font-family: wingdings; font-style: italic;"><font size="4">Entonces, al reemplazar en la fórmula nos queda</font> : </span><br style="font-family: wingdings; font-style: italic;" /><span style="font-family: wingdings; font-style: italic;"><span style="font-weight: bold;">M=<span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#a«/mi»«mo»·«/mo»«msup»«mfenced»«mrow»«mn»1«/mn»«mo»+«/mo»«mfrac»«mi»#i1«/mi»«mi»#p«/mi»«/mfrac»«/mrow»«/mfenced»«mi»#n«/mi»«/msup»«/math»</span></span></span><br style="font-family: wingdings; font-style: italic;" /><span style="font-family: wingdings; font-style: italic;"><span style="font-weight: bold;">M</span></span><span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»=«/mo»«mi»#sol«/mi»«/math»</span><font size="4" style="font-family: wingdings; font-style: italic;"> </font><font size="4" style="font-family: wingdings; font-style: italic;">(aproximar a la centésima)</font><br style="font-family: wingdings; font-style: italic;" /><br style="font-family: wingdings; font-style: italic;" /><font size="4" style="font-family: wingdings; font-style: italic;">Por tanto, el monto acumulado será de <span class="nolink">«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#sol1«/mi»«/math»</span> U</font><span style="font-family: wingdings; font-style: italic;"><font size="4">F</font>.</span><br style="font-family: times new roman,times,serif; font-style: italic;" /><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"><span style="font-weight: bold;"></span></font><font size="4" style="font-family: times new roman,times,serif; font-style: italic;"><span style="font-weight: bold;"></span></font><span style="font-weight: bold;"></span>
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