Solve 843.5*1-(1+0.41/100)^60/1-(1+frac{0.41{100})}

$$843.5 \times \frac { 1 - ( 1 + \frac { 0.41 } { 100 } ) ^ { 60 } } { 1 - ( 1 + \frac { 0.41 } { 100 } ) }$$

Evaluate

$$57246.193798535510889982800810455599991372494198517579227456832657084387138924211669467246472481787938088069338574304815692329229181929089197185469162629839078501309318804626679586325347169865827445668076206839539024456714413676939397768731035$$

Solution Steps

Expand \frac{0.41}{100} by multiplying both numerator and the denominator by 100.

$$843.5\times \frac{1-\left(1+\frac{41}{10000}\right)^{60}}{1-\left(1+\frac{0.41}{100}\right)}$$

Add 1 and \frac{41}{10000} to get \frac{10041}{10000}.

$$843.5\times \frac{1-\left(\frac{10041}{10000}\right)^{60}}{1-\left(1+\frac{0.41}{100}\right)}$$

Calculate \frac{10041}{10000} to the power of 60 and get \frac{1278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$843.5\times \frac{1-\frac{1278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{1-\left(1+\frac{0.41}{100}\right)}$$

Subtract \frac{1278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} from 1 to get -\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$843.5\times \frac{-\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{1-\left(1+\frac{0.41}{100}\right)}$$

Expand \frac{0.41}{100} by multiplying both numerator and the denominator by 100.

$$843.5\times \frac{-\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{1-\left(1+\frac{41}{10000}\right)}$$

Add 1 and \frac{41}{10000} to get \frac{10041}{10000}.

$$843.5\times \frac{-\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{1-\frac{10041}{10000}}$$

Subtract \frac{10041}{10000} from 1 to get -\frac{41}{10000}.

$$843.5\times \frac{-\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{-\frac{41}{10000}}$$

Divide -\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by -\frac{41}{10000} by multiplying -\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of -\frac{41}{10000}.

$$843.5\left(-\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\right)\left(-\frac{10000}{41}\right)$$

Multiply -\frac{278256543656189205274368089298005880218882307307554327009570852275098977201647027676130065841345975751228315694314937456240130218904456746542336008970696313244641811745226993937526892618134498983434782587371715601660074130522911027303914401}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and -\frac{10000}{41} to get \frac{6786744967224126957911416812146484883387373348964739683160264689636560419552366528686099166862096969542154041324754572103417810217181871866886244121236495444991263701103097413110412015076451194717921526521261356138050588549339293348875961}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$843.5\times \frac{6786744967224126957911416812146484883387373348964739683160264689636560419552366528686099166862096969542154041324754572103417810217181871866886244121236495444991263701103097413110412015076451194717921526521261356138050588549339293348875961}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 843.5 and \frac{6786744967224126957911416812146484883387373348964739683160264689636560419552366528686099166862096969542154041324754572103417810217181871866886244121236495444991263701103097413110412015076451194717921526521261356138050588549339293348875961}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{11449238759707102177996560162091119998274498839703515845491366531416877427784842333893449294496357587617613867714860963138465845836385817839437093832525967815700261863760925335917265069433973165489133615241367907804891342882735387879553746207}{200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{11449238759707102177996560162091119998274498839703515845491366531416877427784842333893449294496357587617613867714860963138465845836385817839437093832525967815700261863760925335917265069433973165489133615241367907804891342882735387879553746207}{200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$