Whakaoti i te 1600*(1/0.08-1/0.08*1.08^12)

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

Aromātai

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

Ngā Upane Otinga

Whakarohaina te \frac{1}{0.08} mā te whakarea i te taurunga me te tauraro ki te 100.

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

Whakahekea te hautanga \frac{100}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Tātaihia te 1.08 mā te pū o 12, kia riro ko 2.518170116818978404827136.

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

Whakareatia te 0.08 ki te 2.518170116818978404827136, ka 0.20145360934551827238617088.

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

Whakarohaina te \frac{1}{0.20145360934551827238617088} mā te whakarea i te taurunga me te tauraro ki te 100000000000000000000000000.

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

Whakahekea te hautanga \frac{100000000000000000000000000}{20145360934551827238617088} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 67108864.

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

Ko te maha noa iti rawa atu o 2 me 300189270593998242 ko 300189270593998242. Me tahuri \frac{25}{2} me \frac{1490116119384765625}{300189270593998242} ki te hautau me te tautūnga 300189270593998242.

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

Tā te mea he rite te tauraro o \frac{3752365882424978025}{300189270593998242} me \frac{1490116119384765625}{300189270593998242}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1490116119384765625 i te 3752365882424978025, ka 2262249763040212400.

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

Whakahekea te hautanga \frac{2262249763040212400}{300189270593998242} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Tuhia te 1600\times \frac{1131124881520106200}{150094635296999121} hei hautanga kotahi.

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

Whakareatia te 1600 ki te 1131124881520106200, ka 1809799810432169920000.

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

Tauwehe

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