Solve S=5673{left(1+frac{0.05/12right)}^72-1}{0.05/12}

$$S = 5673 \frac{ { \left(1+ \frac{ 0.05 }{ 12 } \right) }^{ 72 } -1 }{ \frac{ 0.05 }{ 12 } }$$

Solve for S

$$S = \frac{1565843807963601546865877749122462330445204766504937997324779090192906619556580834841203555820606666926759164155408141012118702142296774870969664416612663293322271188634047971}{3295163032920035185459242585677485235658520287317994030252421702669666064972891025383853120081100800000000000000000000000000000000000000000000000000000000000000000000000} = 475194\frac{2.105698198415851 \times 10^{168}}{3.295163032920035 \times 10^{168}} \approx 475194.639027015$$

Steps for Solving Linear Equation

Expand \frac{0.05}{12} by multiplying both numerator and the denominator by 100.

$$S=5673\times \frac{\left(1+\frac{5}{1200}\right)^{72}-1}{\frac{0.05}{12}}$$

Reduce the fraction \frac{5}{1200} to lowest terms by extracting and canceling out 5.

$$S=5673\times \frac{\left(1+\frac{1}{240}\right)^{72}-1}{\frac{0.05}{12}}$$

Add 1 and \frac{1}{240} to get \frac{241}{240}.

$$S=5673\times \frac{\left(\frac{241}{240}\right)^{72}-1}{\frac{0.05}{12}}$$

Calculate \frac{241}{240} to the power of 72 and get \frac{3200568048939655130921388532191471194341085831884787535374963663041623670194855327192928215691923335876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000}.

$$S=5673\times \frac{\frac{3200568048939655130921388532191471194341085831884787535374963663041623670194855327192928215691923335876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000}-1}{\frac{0.05}{12}}$$

Subtract 1 from \frac{3200568048939655130921388532191471194341085831884787535374963663041623670194855327192928215691923335876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000}.

$$S=5673\times \frac{\frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{0.05}{12}}$$

Expand \frac{0.05}{12} by multiplying both numerator and the denominator by 100.

$$S=5673\times \frac{\frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{5}{1200}}$$

Reduce the fraction \frac{5}{1200} to lowest terms by extracting and canceling out 5.

$$S=5673\times \frac{\frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{1}{240}}$$

Divide \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000} by \frac{1}{240} by multiplying \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{1}{240}.

$$S=5673\times \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000}\times 240$$

Multiply \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{2372517383702425333530654661687789369674134606868955701781743625922159566780481538276374246458392576000000000000000000000000000000000000000000000000000000000000000000000000} and 240 to get \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{9885489098760105556377727757032455706975560861953982090757265108008998194918673076151559360243302400000000000000000000000000000000000000000000000000000000000000000000000}.

$$S=5673\times \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{9885489098760105556377727757032455706975560861953982090757265108008998194918673076151559360243302400000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 5673 and \frac{828050665237229797390733870503681824666951225015831833593220037119464103414373788916553969233530759876657410975890079858338816574456253236895644852783005443322195234602881}{9885489098760105556377727757032455706975560861953982090757265108008998194918673076151559360243302400000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{1565843807963601546865877749122462330445204766504937997324779090192906619556580834841203555820606666926759164155408141012118702142296774870969664416612663293322271188634047971}{3295163032920035185459242585677485235658520287317994030252421702669666064972891025383853120081100800000000000000000000000000000000000000000000000000000000000000000000000}.

$$S=\frac{1565843807963601546865877749122462330445204766504937997324779090192906619556580834841203555820606666926759164155408141012118702142296774870969664416612663293322271188634047971}{3295163032920035185459242585677485235658520287317994030252421702669666064972891025383853120081100800000000000000000000000000000000000000000000000000000000000000000000000}$$

Assign S

$$S≔\frac{1565843807963601546865877749122462330445204766504937997324779090192906619556580834841203555820606666926759164155408141012118702142296774870969664416612663293322271188634047971}{3295163032920035185459242585677485235658520287317994030252421702669666064972891025383853120081100800000000000000000000000000000000000000000000000000000000000000000000000}$$