Solve 1-(1+0.4/12)^-84/frac{0.04{12}}*1036.4

$$\frac { 1 - ( 1 + \frac { 0.4 } { 12 } ) ^ { - 84 } } { \frac { 0.04 } { 12 } } \times 1036.4$$

Evaluate

$$\frac{54760680452594927893575994785245988775210895539006732472294965055927333029917688358491896833286722486818420419687658654161459997320}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}\approx 291129.727536998$$

Solution Steps

Expand \frac{0.4}{12} by multiplying both numerator and the denominator by 10.

$$\frac{1-\left(1+\frac{4}{120}\right)^{-84}}{\frac{0.04}{12}}\times 1036.4$$

Reduce the fraction \frac{4}{120} to lowest terms by extracting and canceling out 4.

$$\frac{1-\left(1+\frac{1}{30}\right)^{-84}}{\frac{0.04}{12}}\times 1036.4$$

Add 1 and \frac{1}{30} to get \frac{31}{30}.

$$\frac{1-\left(\frac{31}{30}\right)^{-84}}{\frac{0.04}{12}}\times 1036.4$$

Calculate \frac{31}{30} to the power of -84 and get \frac{11972515182562019788602740026717047105681000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}.

$$\frac{1-\frac{11972515182562019788602740026717047105681000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}}{\frac{0.04}{12}}\times 1036.4$$

Subtract \frac{11972515182562019788602740026717047105681000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921} from 1 to get \frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}.

$$\frac{\frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}}{\frac{0.04}{12}}\times 1036.4$$

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

$$\frac{\frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}}{\frac{4}{1200}}\times 1036.4$$

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

$$\frac{\frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}}{\frac{1}{300}}\times 1036.4$$

Divide \frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921} by \frac{1}{300} by multiplying \frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921} by the reciprocal of \frac{1}{300}.

$$\frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}\times 300\times 1036.4$$

Multiply \frac{176124663748214743000051443410671519282165494464835753480943538710688707802385463651395525644174458017555706997580273556417921}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921} and 300 to get \frac{52837399124464422900015433023201455784649648339450726044283061613206612340715639095418657693252337405266712099274082066925376300}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}.

$$\frac{52837399124464422900015433023201455784649648339450726044283061613206612340715639095418657693252337405266712099274082066925376300}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}\times 1036.4$$

Multiply \frac{52837399124464422900015433023201455784649648339450726044283061613206612340715639095418657693252337405266712099274082066925376300}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921} and 1036.4 to get \frac{54760680452594927893575994785245988775210895539006732472294965055927333029917688358491896833286722486818420419687658654161459997320}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}.

$$\frac{54760680452594927893575994785245988775210895539006732472294965055927333029917688358491896833286722486818420419687658654161459997320}{188097178930776762788654183437388566387846494464835753480943538710688707802385463651395525644174458017555706997580273556417921}$$