Matemàtiques comercials/anualitats de capitalització
Capital final AC
Creiem que podem estalviar #pagaments #mensualitat €. Quin capital haurem estalviat, si ho anem ingressant al banc durant #temps anys amb un interès del #redit % ?]]>
1.0000000
1.0000000
0
0
#capital]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>a</mi><mi>p</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question>
Capital final AC.
En Pau vol conèixer quina quantitat rebrà d'aquí a #temps anys si #pagaments ingressa #mensualitat € al #redit % d'interès compost. Troba-la.]]>
1.0000000
1.0000000
0
0
#capital]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>a</mi><mi>p</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
Capital final AC.
L'Ulisses decideix obrir un pla de jubilació per d'aquí a #temps anys. Un banc li ofereix #redit % anual amb ingressos de #mensualitat € #pagas . Quin capital haurà obtingut al final dels #temps anys?]]>
1.0000000
1.0000000
0
0
#capital]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>rr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagas</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>rr</mi><mo>)</mo><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>a</mi><mi>p</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question>
Capital final AC.
Una família ha obert un compte al que ingressa #pagaments #mensualitat €. El banc els hi dóna una taxa d’interès del #redit %. Calcula la quantitat que tindrà acumulada després de #temps anys.]]>
1.0000000
1.0000000
0
0
#capital]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>a</mi><mi>p</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
mensualitat AC
Per tal d'aconseguir un capital de #capital €, el banc ens proposa que ingressem una quantitat fixa #pagaments durant #temps anys amb un interès de #redit % . Quina quantitat de diners haurem d'ingressar #pagaments ? ]]>
1.0000000
1.0000000
0
0
#mensualitat]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>t</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question>
mensualitat AC.
Els pares de la Verònica han obert un pla d'estalvis per la seva filla. Volen assegurar-se que d'aquí a #temps anys la seva filla disposi d'un capital de #capital €. L'entitat els assegura un #redit % dínterès compost anual amb ingressos #pagaments . Quina quantitat han d'ingressar al començament de cada termini?]]>
1.0000000
1.0000000
0
0
#mensualitat]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>rr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensuals</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensuals</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestrals</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestrals</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestrals</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anuals</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mi>rr</mi><mo>)</mo><mo>.</mo><mo>.</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>rr</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>t</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question>
mensualitat AC.
Quina quantitat ha de pagar la Glòria #pagaments per aconseguir un capital de #capital € en #temps anys si l'interès és de #redit %?]]>
1.0000000
1.0000000
0
0
#mensualitat]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>rr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>rr</mi><mo>)</mo><mo>.</mo><mo>.</mo><mo>(</mo><mn>4</mn><mo>*</mo><mi>rr</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nota</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>mensualitat</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>t</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
mensualitat AC.
Un banc li ha ofert a la Nina un pla de jubilació amb un rèdit del #redit % fixe al llarg de tota la vida del pla. La Nina està interessada en obtenir un capital final de #capital € d'aquí a #temps anys que és el temps en el que pensa jubilar-se. Quina quantitat haurà de pagar #pagaments per aconseguir-lo?]]>
1.0000000
1.0000000
0
0
#mensualitat]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>rr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>rr</mi><mo>)</mo><mo>.</mo><mo>.</mo><mo>(</mo><mn>4</mn><mo>*</mo><mi>rr</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi>u</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi>t</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
Temps AC.
Calcula el temps necessari perquè ingressant #mensualitat € #pagaments a un interès del #redit % obtinguem #capital €.]]>
1.0000000
1.0000000
0
0
#temps]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>capital</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>40</mn><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mesos</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>periode</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>paraules</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>mensualment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>bimensualment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mo> </mo><mi>trimestralment</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatrimestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>semestralment</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>anualment</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pagaments</mi><mo>=</mo><mi>paraules</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temps</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cicle</mi><mo>=</mo><mn>12</mn><mo>/</mo><mi>mesos</mi><mo>.</mo><mi>periode</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>redit2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>redit</mi><mo>/</mo><mi>cicle</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>capital</mi><mo>*</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mi>mensualitat</mi><mo>/</mo><mo>(</mo><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mrow><mo>(</mo><mi>cicle</mi><mo>*</mo><mi>temps</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>-</mo><mfenced><mrow><mn>1</mn><mo>+</mo><mi>redit2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mensualitat</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>mensualitat</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>t</mi><mi mathvariant="normal">e</mi><mi>m</mi><mi>p</mi><mi>s</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">10</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>