Solve 1600*(1/0.08-1/0.08*1.08^12)

$$1600 \times ( \frac{ 1 }{ 0.08 } - \frac{ 1 }{ 0.08 \times { 1.08 }^{ 12 } } )$$

Evaluate

$$\frac{1809799810432169920000}{150094635296999121}\approx 12057.72482708$$

Solution Steps

Expand \frac{1}{0.08} by multiplying both numerator and the denominator by 100.

$$1600\left(\frac{100}{8}-\frac{1}{0.08\times 1.08^{12}}\right)$$

Reduce the fraction \frac{100}{8} to lowest terms by extracting and canceling out 4.

$$1600\left(\frac{25}{2}-\frac{1}{0.08\times 1.08^{12}}\right)$$

Calculate 1.08 to the power of 12 and get 2.518170116818978404827136.

$$1600\left(\frac{25}{2}-\frac{1}{0.08\times 2.518170116818978404827136}\right)$$

Multiply 0.08 and 2.518170116818978404827136 to get 0.20145360934551827238617088.

$$1600\left(\frac{25}{2}-\frac{1}{0.20145360934551827238617088}\right)$$

Expand \frac{1}{0.20145360934551827238617088} by multiplying both numerator and the denominator by 100000000000000000000000000.

$$1600\left(\frac{25}{2}-\frac{100000000000000000000000000}{20145360934551827238617088}\right)$$

Reduce the fraction \frac{100000000000000000000000000}{20145360934551827238617088} to lowest terms by extracting and canceling out 67108864.

$$1600\left(\frac{25}{2}-\frac{1490116119384765625}{300189270593998242}\right)$$

Least common multiple of 2 and 300189270593998242 is 300189270593998242. Convert \frac{25}{2} and \frac{1490116119384765625}{300189270593998242} to fractions with denominator 300189270593998242.

$$1600\left(\frac{3752365882424978025}{300189270593998242}-\frac{1490116119384765625}{300189270593998242}\right)$$

Since \frac{3752365882424978025}{300189270593998242} and \frac{1490116119384765625}{300189270593998242} have the same denominator, subtract them by subtracting their numerators.

$$1600\times \frac{3752365882424978025-1490116119384765625}{300189270593998242}$$

Subtract 1490116119384765625 from 3752365882424978025 to get 2262249763040212400.

$$1600\times \frac{2262249763040212400}{300189270593998242}$$

Reduce the fraction \frac{2262249763040212400}{300189270593998242} to lowest terms by extracting and canceling out 2.

$$1600\times \frac{1131124881520106200}{150094635296999121}$$

Express 1600\times \frac{1131124881520106200}{150094635296999121} as a single fraction.

$$\frac{1600\times 1131124881520106200}{150094635296999121}$$

Multiply 1600 and 1131124881520106200 to get 1809799810432169920000.

$$\frac{1809799810432169920000}{150094635296999121}$$

Factor

$$\frac{7 \cdot 13 \cdot 97 \cdot 677 \cdot 2029 \cdot 466441 \cdot 2 ^ {9} \cdot 5 ^ {4}}{3 ^ {36}} = 12057\frac{1.087926562513521 \times 10^{17}}{1.5009463529699913 \times 10^{17}} = 12057.724827080168$$