Solve left(20000-frac{20000/1-{left(frac{1{1.06}right)}^20}0.061-{left(frac{1/1.06right)}^5}{0.06}right)1.06^2}{1-{left(1/1.06right)}^12}0.06

$$\frac{ \left( 20000- \frac{ 20000 }{ 1- { \left( \frac{ 1 }{ 1.06 } \right) }^{ 20 } } 0.06 \frac{ 1- { \left( \frac{ 1 }{ 1.06 } \right) }^{ 5 } }{ 0.06 } \right) { 1.06 }^{ 2 } }{ 1- { \left( \frac{ 1 }{ 1.06 } \right) }^{ 12 } } 0.06$$

Evaluate

$$\frac{3495636837040248090426856348412041137950000000}{2061093626544877439898731059925262989963881}\approx 1696.010696467$$

Solution Steps

Expand \frac{1}{1.06} by multiplying both numerator and the denominator by 100.

$$\frac{\left(20000-\frac{20000}{1-\left(\frac{100}{106}\right)^{20}}\times 0.06\times \frac{1-\left(\frac{1}{1.06}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Reduce the fraction \frac{100}{106} to lowest terms by extracting and canceling out 2.

$$\frac{\left(20000-\frac{20000}{1-\left(\frac{50}{53}\right)^{20}}\times 0.06\times \frac{1-\left(\frac{1}{1.06}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Calculate \frac{50}{53} to the power of 20 and get \frac{9536743164062500000000000000000000}{30585627290848204916791848989276401}.

$$\frac{\left(20000-\frac{20000}{1-\frac{9536743164062500000000000000000000}{30585627290848204916791848989276401}}\times 0.06\times \frac{1-\left(\frac{1}{1.06}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Subtract \frac{9536743164062500000000000000000000}{30585627290848204916791848989276401} from 1 to get \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401}.

$$\frac{\left(20000-\frac{20000}{\frac{21048884126785704916791848989276401}{30585627290848204916791848989276401}}\times 0.06\times \frac{1-\left(\frac{1}{1.06}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Divide 20000 by \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401} by multiplying 20000 by the reciprocal of \frac{21048884126785704916791848989276401}{30585627290848204916791848989276401}.

$$\frac{\left(20000-20000\times \frac{30585627290848204916791848989276401}{21048884126785704916791848989276401}\times 0.06\times \frac{1-\left(\frac{1}{1.06}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Multiply 20000 and \frac{30585627290848204916791848989276401}{21048884126785704916791848989276401} to get \frac{611712545816964098335836979785528020000}{21048884126785704916791848989276401}.

$$\frac{\left(20000-\frac{611712545816964098335836979785528020000}{21048884126785704916791848989276401}\times 0.06\times \frac{1-\left(\frac{1}{1.06}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Multiply \frac{611712545816964098335836979785528020000}{21048884126785704916791848989276401} and 0.06 to get \frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{1-\left(\frac{1}{1.06}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Expand \frac{1}{1.06} by multiplying both numerator and the denominator by 100.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{1-\left(\frac{100}{106}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Reduce the fraction \frac{100}{106} to lowest terms by extracting and canceling out 2.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{1-\left(\frac{50}{53}\right)^{5}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Calculate \frac{50}{53} to the power of 5 and get \frac{312500000}{418195493}.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{1-\frac{312500000}{418195493}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Subtract \frac{312500000}{418195493} from 1 to get \frac{105695493}{418195493}.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{\frac{105695493}{418195493}}{0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Express \frac{\frac{105695493}{418195493}}{0.06} as a single fraction.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{105695493}{418195493\times 0.06}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Multiply 418195493 and 0.06 to get 25091729.58.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{105695493}{25091729.58}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Expand \frac{105695493}{25091729.58} by multiplying both numerator and the denominator by 100.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{10569549300}{2509172958}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Reduce the fraction \frac{10569549300}{2509172958} to lowest terms by extracting and canceling out 6.

$$\frac{\left(20000-\frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467}\times \frac{1761591550}{418195493}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Multiply \frac{12234250916339281966716739595710560400}{7016294708928568305597282996425467} and \frac{1761591550}{418195493} to get \frac{1462743037780572394489763140000}{199146468116532697536988157}.

$$\frac{\left(20000-\frac{1462743037780572394489763140000}{199146468116532697536988157}\right)\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Subtract \frac{1462743037780572394489763140000}{199146468116532697536988157} from 20000 to get \frac{2520186324550081556250000000000}{199146468116532697536988157}.

$$\frac{\frac{2520186324550081556250000000000}{199146468116532697536988157}\times 1.06^{2}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Calculate 1.06 to the power of 2 and get 1.1236.

$$\frac{\frac{2520186324550081556250000000000}{199146468116532697536988157}\times 1.1236}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Multiply \frac{2520186324550081556250000000000}{199146468116532697536988157} and 1.1236 to get \frac{2831681354264471636602500000000}{199146468116532697536988157}.

$$\frac{\frac{2831681354264471636602500000000}{199146468116532697536988157}}{1-\left(\frac{1}{1.06}\right)^{12}}\times 0.06$$

Expand \frac{1}{1.06} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{2831681354264471636602500000000}{199146468116532697536988157}}{1-\left(\frac{100}{106}\right)^{12}}\times 0.06$$

Reduce the fraction \frac{100}{106} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2831681354264471636602500000000}{199146468116532697536988157}}{1-\left(\frac{50}{53}\right)^{12}}\times 0.06$$

Calculate \frac{50}{53} to the power of 12 and get \frac{244140625000000000000}{491258904256726154641}.

$$\frac{\frac{2831681354264471636602500000000}{199146468116532697536988157}}{1-\frac{244140625000000000000}{491258904256726154641}}\times 0.06$$

Subtract \frac{244140625000000000000}{491258904256726154641} from 1 to get \frac{247118279256726154641}{491258904256726154641}.

$$\frac{\frac{2831681354264471636602500000000}{199146468116532697536988157}}{\frac{247118279256726154641}{491258904256726154641}}\times 0.06$$

Divide \frac{2831681354264471636602500000000}{199146468116532697536988157} by \frac{247118279256726154641}{491258904256726154641} by multiplying \frac{2831681354264471636602500000000}{199146468116532697536988157} by the reciprocal of \frac{247118279256726154641}{491258904256726154641}.

$$\frac{2831681354264471636602500000000}{199146468116532697536988157}\times \frac{491258904256726154641}{247118279256726154641}\times 0.06$$

Multiply \frac{2831681354264471636602500000000}{199146468116532697536988157} and \frac{491258904256726154641}{247118279256726154641} to get \frac{174781841852012404521342817420602056897500000000}{6183280879634632319696193179775788969891643}.

$$\frac{174781841852012404521342817420602056897500000000}{6183280879634632319696193179775788969891643}\times 0.06$$

Multiply \frac{174781841852012404521342817420602056897500000000}{6183280879634632319696193179775788969891643} and 0.06 to get \frac{3495636837040248090426856348412041137950000000}{2061093626544877439898731059925262989963881}.

$$\frac{3495636837040248090426856348412041137950000000}{2061093626544877439898731059925262989963881}$$

Factor

$$\frac{50663376294511 \cdot 2 ^ {7} \cdot 5 ^ {8} \cdot 53 ^ {14}}{11 \cdot 13 \cdot 151 \cdot 2659 \cdot 4271 \cdot 547537 \cdot 51336168838861 \cdot 103 ^ {2} \cdot 5309 ^ {2}} = 1696\frac{2.2046420136128093 \times 10^{40}}{2.0610936265448774 \times 10^{42}} = 1696.0106964670854$$