Solve 200/0.12*(1-1/(1.12)^10)

$$\frac { 200 } { 0.12 } \times ( 1 - \frac { 1 } { ( 1.12 ) ^ { 10 } } )$$

Evaluate

$$\frac{41839444803083125}{37024595836928}\approx 1130.044605682$$

Solution Steps

Expand \frac{200}{0.12} by multiplying both numerator and the denominator by 100.

$$\frac{20000}{12}\left(1-\frac{1}{1.12^{10}}\right)$$

Reduce the fraction \frac{20000}{12} to lowest terms by extracting and canceling out 4.

$$\frac{5000}{3}\left(1-\frac{1}{1.12^{10}}\right)$$

Calculate 1.12 to the power of 10 and get 3.10584820834420916224.

$$\frac{5000}{3}\left(1-\frac{1}{3.10584820834420916224}\right)$$

Expand \frac{1}{3.10584820834420916224} by multiplying both numerator and the denominator by 100000000000000000000.

$$\frac{5000}{3}\left(1-\frac{100000000000000000000}{310584820834420916224}\right)$$

Reduce the fraction \frac{100000000000000000000}{310584820834420916224} to lowest terms by extracting and canceling out 1048576.

$$\frac{5000}{3}\left(1-\frac{95367431640625}{296196766695424}\right)$$

Convert 1 to fraction \frac{296196766695424}{296196766695424}.

$$\frac{5000}{3}\left(\frac{296196766695424}{296196766695424}-\frac{95367431640625}{296196766695424}\right)$$

Since \frac{296196766695424}{296196766695424} and \frac{95367431640625}{296196766695424} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5000}{3}\times \frac{296196766695424-95367431640625}{296196766695424}$$

Subtract 95367431640625 from 296196766695424 to get 200829335054799.

$$\frac{5000}{3}\times \frac{200829335054799}{296196766695424}$$

Multiply \frac{5000}{3} times \frac{200829335054799}{296196766695424} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5000\times 200829335054799}{3\times 296196766695424}$$

Do the multiplications in the fraction \frac{5000\times 200829335054799}{3\times 296196766695424}.

$$\frac{1004146675273995000}{888590300086272}$$

Reduce the fraction \frac{1004146675273995000}{888590300086272} to lowest terms by extracting and canceling out 24.

$$\frac{41839444803083125}{37024595836928}$$

Factor

$$\frac{11 \cdot 31 \cdot 53 \cdot 46271 \cdot 80051 \cdot 5 ^ {4}}{2 ^ {17} \cdot 7 ^ {10}} = 1130\frac{1651507354488}{37024595836928} = 1130.0446056821731$$