Solve 200[0.5875%(1+0.5875%)^36/(1+0.5875%)^36-1]

$$200 [ \frac { 0.5875 \% ( 1 + 0.5875 \% ) ^ { 36 } } { ( 1 + 0.5875 \% ) ^ { 36 } - 1 } ]$$

Evaluate

$$\frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{64838968276894717199507844252353034029020066342397125948790438218916639215335496216604763975666679618602127598181171565865207175456649221720}\approx 6.179992557$$

Solution Steps

Expand \frac{0.5875}{100} by multiplying both numerator and the denominator by 10000.

$$200\times \frac{\frac{5875}{1000000}\left(1+\frac{0.5875}{100}\right)^{36}}{\left(1+\frac{0.5875}{100}\right)^{36}-1}$$

Reduce the fraction \frac{5875}{1000000} to lowest terms by extracting and canceling out 125.

$$200\times \frac{\frac{47}{8000}\left(1+\frac{0.5875}{100}\right)^{36}}{\left(1+\frac{0.5875}{100}\right)^{36}-1}$$

Expand \frac{0.5875}{100} by multiplying both numerator and the denominator by 10000.

$$200\times \frac{\frac{47}{8000}\left(1+\frac{5875}{1000000}\right)^{36}}{\left(1+\frac{0.5875}{100}\right)^{36}-1}$$

Reduce the fraction \frac{5875}{1000000} to lowest terms by extracting and canceling out 125.

$$200\times \frac{\frac{47}{8000}\left(1+\frac{47}{8000}\right)^{36}}{\left(1+\frac{0.5875}{100}\right)^{36}-1}$$

Add 1 and \frac{47}{8000} to get \frac{8047}{8000}.

$$200\times \frac{\frac{47}{8000}\times \left(\frac{8047}{8000}\right)^{36}}{\left(1+\frac{0.5875}{100}\right)^{36}-1}$$

Calculate \frac{8047}{8000} to the power of 36 and get \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$200\times \frac{\frac{47}{8000}\times \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(1+\frac{0.5875}{100}\right)^{36}-1}$$

Multiply \frac{47}{8000} and \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$200\times \frac{\frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(1+\frac{0.5875}{100}\right)^{36}-1}$$

Expand \frac{0.5875}{100} by multiplying both numerator and the denominator by 10000.

$$200\times \frac{\frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(1+\frac{5875}{1000000}\right)^{36}-1}$$

Reduce the fraction \frac{5875}{1000000} to lowest terms by extracting and canceling out 125.

$$200\times \frac{\frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(1+\frac{47}{8000}\right)^{36}-1}$$

Add 1 and \frac{47}{8000} to get \frac{8047}{8000}.

$$200\times \frac{\frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(\frac{8047}{8000}\right)^{36}-1}$$

Calculate \frac{8047}{8000} to the power of 36 and get \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$200\times \frac{\frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}-1}$$

Subtract 1 from \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{76185787725351292709421716996514814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$200\times \frac{\frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{76185787725351292709421716996514814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}$$

Divide \frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by \frac{76185787725351292709421716996514814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by multiplying \frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{76185787725351292709421716996514814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$200\times \frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{76185787725351292709421716996514814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}$$

Multiply \frac{18833104045037566916151153665920228304252633163758881280521951950639671400666902778561998090556192381937302496609555199724906066264593453269487}{2596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and \frac{324518553658426726783156020576256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{76185787725351292709421716996514814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521} to get \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{12967793655378943439901568850470606805804013268479425189758087643783327843067099243320952795133335923720425519636234313173041435091329844344000}.

$$200\times \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{12967793655378943439901568850470606805804013268479425189758087643783327843067099243320952795133335923720425519636234313173041435091329844344000}$$

Multiply 200 and \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{12967793655378943439901568850470606805804013268479425189758087643783327843067099243320952795133335923720425519636234313173041435091329844344000} to get \frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{64838968276894717199507844252353034029020066342397125948790438218916639215335496216604763975666679618602127598181171565865207175456649221720}.

$$\frac{400704341383778019492577737572770814984098577952316622989828764907227051078019208054510597671408348551857499927862876589891618431161562835521}{64838968276894717199507844252353034029020066342397125948790438218916639215335496216604763975666679618602127598181171565865207175456649221720}$$