Solve 11000((1+0.06/12)^60-1/frac{0.06{12}})

$$11000 ( \frac { ( 1 + \frac { 0.06 } { 12 } ) ^ { 60 } - 1 } { \frac { 0.06 } { 12 } } )$$

Evaluate

$$767470.335608495352561220179366654686049859321263871498985304648889756368185599153238075266354996530904933589538434269372879385014859186105694310864322460474795661866664886474609375$$

Solution Steps

Expand \frac{0.06}{12} by multiplying both numerator and the denominator by 100.

$$11000\times \frac{\left(1+\frac{6}{1200}\right)^{60}-1}{\frac{0.06}{12}}$$

Reduce the fraction \frac{6}{1200} to lowest terms by extracting and canceling out 6.

$$11000\times \frac{\left(1+\frac{1}{200}\right)^{60}-1}{\frac{0.06}{12}}$$

Add 1 and \frac{1}{200} to get \frac{201}{200}.

$$11000\times \frac{\left(\frac{201}{200}\right)^{60}-1}{\frac{0.06}{12}}$$

Calculate \frac{201}{200} to the power of 60 and get \frac{1555118347366332552993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$11000\times \frac{\frac{1555118347366332552993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}-1}{\frac{0.06}{12}}$$

Subtract 1 from \frac{1555118347366332552993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$11000\times \frac{\frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{0.06}{12}}$$

Expand \frac{0.06}{12} by multiplying both numerator and the denominator by 100.

$$11000\times \frac{\frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{6}{1200}}$$

Reduce the fraction \frac{6}{1200} to lowest terms by extracting and canceling out 6.

$$11000\times \frac{\frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{1}{200}}$$

Divide \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by \frac{1}{200} by multiplying \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{1}{200}.

$$11000\times \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times 200$$

Multiply \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{1152921504606846976000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and 200 to get \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{5764607523034234880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$11000\times \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{5764607523034234880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 11000 and \frac{402196842759485576993460339037447094912765281420703829003302194049085925827095061955700754109949900806192137427690816337611504329830812001}{5764607523034234880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{4424165270354341346928063729411918044040418095627742119036324134539945184098045681512708295209448908868113511704598979713726547628138932011}{5764607523034234880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{4424165270354341346928063729411918044040418095627742119036324134539945184098045681512708295209448908868113511704598979713726547628138932011}{5764607523034234880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$