Lutasin ang 20000*(1/0.08-1/0.08*1.08^12)div12=

$$20000 \times ( \frac{ 1 }{ 0.08 } - \frac{ 1 }{ 0.08 \times { 1.08 }^{ 12 } } ) \div 12=$$

I-evaluate

$$\frac{5655624407600531000000}{450283905890997363}\approx 12560.130028209$$

Mga Hakbang ng Solution

I-expand ang \frac{1}{0.08} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 100.

$$\frac{20000\left(\frac{100}{8}-\frac{1}{0.08\times 1.08^{12}}\right)}{12}$$

Bawasan ang fraction \frac{100}{8} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 4.

$$\frac{20000\left(\frac{25}{2}-\frac{1}{0.08\times 1.08^{12}}\right)}{12}$$

Kalkulahin ang 1.08 sa power ng 12 at kunin ang 2.518170116818978404827136.

$$\frac{20000\left(\frac{25}{2}-\frac{1}{0.08\times 2.518170116818978404827136}\right)}{12}$$

I-multiply ang 0.08 at 2.518170116818978404827136 para makuha ang 0.20145360934551827238617088.

$$\frac{20000\left(\frac{25}{2}-\frac{1}{0.20145360934551827238617088}\right)}{12}$$

I-expand ang \frac{1}{0.20145360934551827238617088} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 100000000000000000000000000.

$$\frac{20000\left(\frac{25}{2}-\frac{100000000000000000000000000}{20145360934551827238617088}\right)}{12}$$

Bawasan ang fraction \frac{100000000000000000000000000}{20145360934551827238617088} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 67108864.

$$\frac{20000\left(\frac{25}{2}-\frac{1490116119384765625}{300189270593998242}\right)}{12}$$

Ang least common multiple ng 2 at 300189270593998242 ay 300189270593998242. I-convert ang \frac{25}{2} at \frac{1490116119384765625}{300189270593998242} sa mga fraction na may denominator na 300189270593998242.

$$\frac{20000\left(\frac{3752365882424978025}{300189270593998242}-\frac{1490116119384765625}{300189270593998242}\right)}{12}$$

Dahil may parehong denominator ang \frac{3752365882424978025}{300189270593998242} at \frac{1490116119384765625}{300189270593998242}, ibawas ang mga ito sa pamamagitan ng pagbawas sa mga numerator ng mga ito.

$$\frac{20000\times \frac{3752365882424978025-1490116119384765625}{300189270593998242}}{12}$$

I-subtract ang 1490116119384765625 mula sa 3752365882424978025 para makuha ang 2262249763040212400.

$$\frac{20000\times \frac{2262249763040212400}{300189270593998242}}{12}$$

Bawasan ang fraction \frac{2262249763040212400}{300189270593998242} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 2.

$$\frac{20000\times \frac{1131124881520106200}{150094635296999121}}{12}$$

Ipakita ang 20000\times \frac{1131124881520106200}{150094635296999121} bilang isang single fraction.

$$\frac{\frac{20000\times 1131124881520106200}{150094635296999121}}{12}$$

I-multiply ang 20000 at 1131124881520106200 para makuha ang 22622497630402124000000.

$$\frac{\frac{22622497630402124000000}{150094635296999121}}{12}$$

Ipakita ang \frac{\frac{22622497630402124000000}{150094635296999121}}{12} bilang isang single fraction.

$$\frac{22622497630402124000000}{150094635296999121\times 12}$$

I-multiply ang 150094635296999121 at 12 para makuha ang 1801135623563989452.

$$\frac{22622497630402124000000}{1801135623563989452}$$

Bawasan ang fraction \frac{22622497630402124000000}{1801135623563989452} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 4.

$$\frac{5655624407600531000000}{450283905890997363}$$

I-factor

$$\frac{7 \cdot 13 \cdot 97 \cdot 677 \cdot 2029 \cdot 466441 \cdot 2 ^ {6} \cdot 5 ^ {6}}{3 ^ {37}} = 12560\frac{58549609603938300}{4.502839058909974 \times 10^{17}} = 12560.13002820851$$