Solve 614*1-(1+0.56/100)^24/1-(1+frac{0.56{100})}

$$614 \times \frac { 1 - ( 1 + \frac { 0.56 } { 100 } ) ^ { 24 } } { 1 - ( 1 + \frac { 0.56 } { 100 } ) }$$

Evaluate

$$15725.14251096905958364099021164927899879764296934921138859254608690125588961318367983459708698624$$

Solution Steps

Expand \frac{0.56}{100} by multiplying both numerator and the denominator by 100.

$$614\times \frac{1-\left(1+\frac{56}{10000}\right)^{24}}{1-\left(1+\frac{0.56}{100}\right)}$$

Reduce the fraction \frac{56}{10000} to lowest terms by extracting and canceling out 8.

$$614\times \frac{1-\left(1+\frac{7}{1250}\right)^{24}}{1-\left(1+\frac{0.56}{100}\right)}$$

Add 1 and \frac{7}{1250} to get \frac{1257}{1250}.

$$614\times \frac{1-\left(\frac{1257}{1250}\right)^{24}}{1-\left(1+\frac{0.56}{100}\right)}$$

Calculate \frac{1257}{1250} to the power of 24 and get \frac{242128919761268921920732095989607516012175777452066004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}.

$$614\times \frac{1-\frac{242128919761268921920732095989607516012175777452066004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}}{1-\left(1+\frac{0.56}{100}\right)}$$

Subtract \frac{242128919761268921920732095989607516012175777452066004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000} from 1 to get -\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}.

$$614\times \frac{-\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}}{1-\left(1+\frac{0.56}{100}\right)}$$

Expand \frac{0.56}{100} by multiplying both numerator and the denominator by 100.

$$614\times \frac{-\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}}{1-\left(1+\frac{56}{10000}\right)}$$

Reduce the fraction \frac{56}{10000} to lowest terms by extracting and canceling out 8.

$$614\times \frac{-\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}}{1-\left(1+\frac{7}{1250}\right)}$$

Add 1 and \frac{7}{1250} to get \frac{1257}{1250}.

$$614\times \frac{-\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}}{1-\frac{1257}{1250}}$$

Subtract \frac{1257}{1250} from 1 to get -\frac{7}{1250}.

$$614\times \frac{-\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}}{-\frac{7}{1250}}$$

Divide -\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000} by -\frac{7}{1250} by multiplying -\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000} by the reciprocal of -\frac{7}{1250}.

$$614\left(-\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000}\right)\left(-\frac{1250}{7}\right)$$

Multiply -\frac{30370682947693837153651470819697025499327877061441004729069278396375454401}{211758236813575084767080625169910490512847900390625000000000000000000000000} and -\frac{1250}{7} to get \frac{4338668992527691021950210117099575071332553865920143532724182628053636343}{169406589450860067813664500135928392410278320312500000000000000000000000}.

$$614\times \frac{4338668992527691021950210117099575071332553865920143532724182628053636343}{169406589450860067813664500135928392410278320312500000000000000000000000}$$

Multiply 614 and \frac{4338668992527691021950210117099575071332553865920143532724182628053636343}{169406589450860067813664500135928392410278320312500000000000000000000000} to get \frac{1331971380706001143738714505949569546899094036837484064546324066812466357301}{84703294725430033906832250067964196205139160156250000000000000000000000}.

$$\frac{1331971380706001143738714505949569546899094036837484064546324066812466357301}{84703294725430033906832250067964196205139160156250000000000000000000000}$$