Solve 96.341.004left(1-1.004^10right)/1-1.004

$$96.34 \frac{ 1.004 \left( 1- { 1.004 }^{ 10 } \right) }{ 1-1.004 }$$

Evaluate

$$984.85118374083225956043590870237184$$

Solution Steps

Calculate 1.004 to the power of 10 and get 1.040727734018910129031742488576.

$$96.34\times \frac{1.004\left(1-1.040727734018910129031742488576\right)}{1-1.004}$$

Subtract 1.040727734018910129031742488576 from 1 to get -0.040727734018910129031742488576.

$$96.34\times \frac{1.004\left(-0.040727734018910129031742488576\right)}{1-1.004}$$

Multiply 1.004 and -0.040727734018910129031742488576 to get -0.040890644954985769547869458530304.

$$96.34\times \frac{-0.040890644954985769547869458530304}{1-1.004}$$

Subtract 1.004 from 1 to get -0.004.

$$96.34\times \frac{-0.040890644954985769547869458530304}{-0.004}$$

Expand \frac{-0.040890644954985769547869458530304}{-0.004} by multiplying both numerator and the denominator by 1000000000000000000000000000000000.

$$96.34\times \frac{-40890644954985769547869458530304}{-4000000000000000000000000000000}$$

Reduce the fraction \frac{-40890644954985769547869458530304}{-4000000000000000000000000000000} to lowest terms by extracting and canceling out -4194304.

$$96.34\times \frac{9749089468714182269065251}{953674316406250000000000}$$

Convert decimal number 96.34 to fraction \frac{9634}{100}. Reduce the fraction \frac{9634}{100} to lowest terms by extracting and canceling out 2.

$$\frac{4817}{50}\times \frac{9749089468714182269065251}{953674316406250000000000}$$

Multiply \frac{4817}{50} times \frac{9749089468714182269065251}{953674316406250000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4817\times 9749089468714182269065251}{50\times 953674316406250000000000}$$

Do the multiplications in the fraction \frac{4817\times 9749089468714182269065251}{50\times 953674316406250000000000}.

$$\frac{46961363970796215990087314067}{47683715820312500000000000}$$

Factor

$$\frac{3 \cdot 11 \cdot 61 \cdot 167 \cdot 251 \cdot 571 \cdot 2141 \cdot 2741 \cdot 4817 \cdot 34480081}{2 ^ {11} \cdot 5 ^ {32}} = 984\frac{4.0587603608720615 \times 10^{25}}{4.76837158203125 \times 10^{25}} = 984.8511837408323$$