Solve 1.014674/2.87373%-1.4674%(1-(1.014674/1.0287373)^40)

$$\frac { 1.014674 } { 2.87373 \% - 1.4674 \% } ( 1 - ( \frac { 1.014674 } { 1.0287373 } ) ^ { 40 } )$$

Evaluate

$$\frac{948767593449166784728989137169025081278696996697726106961001974037354615901380739114896599569793122839921501382330098570354701444535135141245988353959024597446057782076097360796959272505314093217754905774208627049511181532820659062159952513114778229411262047507862462441207418493780}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401}\approx 30.547830403$$

Solution Steps

Expand \frac{2.87373}{100} by multiplying both numerator and the denominator by 100000.

$$\frac{1.014674}{\frac{287373}{10000000}-\frac{1.4674}{100}}\left(1-\left(\frac{1.014674}{1.0287373}\right)^{40}\right)$$

Expand \frac{1.4674}{100} by multiplying both numerator and the denominator by 10000.

$$\frac{1.014674}{\frac{287373}{10000000}-\frac{14674}{1000000}}\left(1-\left(\frac{1.014674}{1.0287373}\right)^{40}\right)$$

Reduce the fraction \frac{14674}{1000000} to lowest terms by extracting and canceling out 2.

$$\frac{1.014674}{\frac{287373}{10000000}-\frac{7337}{500000}}\left(1-\left(\frac{1.014674}{1.0287373}\right)^{40}\right)$$

Subtract \frac{7337}{500000} from \frac{287373}{10000000} to get \frac{140633}{10000000}.

$$\frac{1.014674}{\frac{140633}{10000000}}\left(1-\left(\frac{1.014674}{1.0287373}\right)^{40}\right)$$

Divide 1.014674 by \frac{140633}{10000000} by multiplying 1.014674 by the reciprocal of \frac{140633}{10000000}.

$$1.014674\times \frac{10000000}{140633}\left(1-\left(\frac{1.014674}{1.0287373}\right)^{40}\right)$$

Multiply 1.014674 and \frac{10000000}{140633} to get \frac{10146740}{140633}.

$$\frac{10146740}{140633}\left(1-\left(\frac{1.014674}{1.0287373}\right)^{40}\right)$$

Expand \frac{1.014674}{1.0287373} by multiplying both numerator and the denominator by 10000000.

$$\frac{10146740}{140633}\left(1-\left(\frac{10146740}{10287373}\right)^{40}\right)$$

Calculate \frac{10146740}{10287373} to the power of 40 and get \frac{17908585567544444022762907786270340249243490856348492874190616170702952529790967595525332552380078354408568329126919437093818993615161049549217985032799769965722964279778991483863959325662069930585275976025719125133897778718364964730185973760000000000000000000000000000000000000000}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401}.

$$\frac{10146740}{140633}\left(1-\frac{17908585567544444022762907786270340249243490856348492874190616170702952529790967595525332552380078354408568329126919437093818993615161049549217985032799769965722964279778991483863959325662069930585275976025719125133897778718364964730185973760000000000000000000000000000000000000000}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401}\right)$$

Subtract \frac{17908585567544444022762907786270340249243490856348492874190616170702952529790967595525332552380078354408568329126919437093818993615161049549217985032799769965722964279778991483863959325662069930585275976025719125133897778718364964730185973760000000000000000000000000000000000000000}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401} from 1 to get \frac{13149842507991401419253073334636691612820176207983186284486109885026648135071843516631475083356695475034018857672634634596401674651100714152412211230633632695095315743451374544036683049949031597487717795444081729486899831128536628108017018448966920088303634027005050063418824458401}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401}.

$$\frac{10146740}{140633}\times \frac{13149842507991401419253073334636691612820176207983186284486109885026648135071843516631475083356695475034018857672634634596401674651100714152412211230633632695095315743451374544036683049949031597487717795444081729486899831128536628108017018448966920088303634027005050063418824458401}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401}$$

Multiply \frac{10146740}{140633} and \frac{13149842507991401419253073334636691612820176207983186284486109885026648135071843516631475083356695475034018857672634634596401674651100714152412211230633632695095315743451374544036683049949031597487717795444081729486899831128536628108017018448966920088303634027005050063418824458401}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401} to get \frac{948767593449166784728989137169025081278696996697726106961001974037354615901380739114896599569793122839921501382330098570354701444535135141245988353959024597446057782076097360796959272505314093217754905774208627049511181532820659062159952513114778229411262047507862462441207418493780}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401}.

$$\frac{948767593449166784728989137169025081278696996697726106961001974037354615901380739114896599569793122839921501382330098570354701444535135141245988353959024597446057782076097360796959272505314093217754905774208627049511181532820659062159952513114778229411262047507862462441207418493780}{31058428075535845442015981120907031862063667064331679158676726055729600664862811112156807635736773829442587186799554071690220668266261763701630196263433402660818280023230366027900642375611101528072993771469800854620797609846901592838202992208966920088303634027005050063418824458401}$$