Solve 1-(1+0.04/12)^-84/frac{0.04{12}}*375

$$\frac { 1 - ( 1 + \frac { 0.04 } { 12 } ) ^ { - 84 } } { \frac { 0.04 } { 12 } } \times 375$$

Evaluate

$$\frac{434396489845174822684132796913397606538085473794118476896551522507154522614598772402569490728278603101448468869977166590188014642518494392857475436633448758853042542866704269752310333937642633533221246698585112500}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}\approx 27434.729175942$$

Solution Steps

Expand \frac{0.04}{12} by multiplying both numerator and the denominator by 100.

$$\frac{1-\left(1+\frac{4}{1200}\right)^{-84}}{\frac{0.04}{12}}\times 375$$

Reduce the fraction \frac{4}{1200} to lowest terms by extracting and canceling out 4.

$$\frac{1-\left(1+\frac{1}{300}\right)^{-84}}{\frac{0.04}{12}}\times 375$$

Add 1 and \frac{1}{300} to get \frac{301}{300}.

$$\frac{1-\left(\frac{301}{300}\right)^{-84}}{\frac{0.04}{12}}\times 375$$

Calculate \frac{301}{300} to the power of -84 and get \frac{11972515182562019788602740026717047105681000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}.

$$\frac{1-\frac{11972515182562019788602740026717047105681000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}}{\frac{0.04}{12}}\times 375$$

Subtract \frac{11972515182562019788602740026717047105681000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201} from 1 to get \frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}.

$$\frac{\frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}}{\frac{0.04}{12}}\times 375$$

Expand \frac{0.04}{12} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}}{\frac{4}{1200}}\times 375$$

Reduce the fraction \frac{4}{1200} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}}{\frac{1}{300}}\times 375$$

Divide \frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201} by \frac{1}{300} by multiplying \frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201} by the reciprocal of \frac{1}{300}.

$$\frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}\times 300\times 375$$

Multiply \frac{3861302131957109534970069305896867613671870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201} and 300 to get \frac{1158390639587132860491020791769060284101561263450982605057470726685745393638930059740185308608742941603862583653272444240501372380049318380953267831022530023608113447644544719339494223833713689421923324529560300}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}.

$$\frac{1158390639587132860491020791769060284101561263450982605057470726685745393638930059740185308608742941603862583653272444240501372380049318380953267831022530023608113447644544719339494223833713689421923324529560300}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}\times 375$$

Multiply \frac{1158390639587132860491020791769060284101561263450982605057470726685745393638930059740185308608742941603862583653272444240501372380049318380953267831022530023608113447644544719339494223833713689421923324529560300}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201} and 375 to get \frac{434396489845174822684132796913397606538085473794118476896551522507154522614598772402569490728278603101448468869977166590188014642518494392857475436633448758853042542866704269752310333937642633533221246698585112500}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}.

$$\frac{434396489845174822684132796913397606538085473794118476896551522507154522614598772402569490728278603101448468869977166590188014642518494392857475436633448758853042542866704269752310333937642633533221246698585112500}{15833817314519129323572809332613914719352870878169942016858235755619151312129766865800617695362476472012875278844241480801671241266831061269844226103408433412027044825481815731131647412779045631406411081765201}$$