Whakaoti i te 20000*(1/0.08-1/0.08*1.08^12)div12=

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

Aromātai

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

Ngā Upane Otinga

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

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

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

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

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

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

Whakareatia te 0.08 ki te 2.518170116818978404827136, ka 0.20145360934551827238617088.

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

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

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

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

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

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.

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

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.

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

Tangohia te 1490116119384765625 i te 3752365882424978025, ka 2262249763040212400.

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

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

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

Tuhia te 20000\times \frac{1131124881520106200}{150094635296999121} hei hautanga kotahi.

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

Whakareatia te 20000 ki te 1131124881520106200, ka 22622497630402124000000.

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

Tuhia te \frac{\frac{22622497630402124000000}{150094635296999121}}{12} hei hautanga kotahi.

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

Whakareatia te 150094635296999121 ki te 12, ka 1801135623563989452.

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

Whakahekea te hautanga \frac{22622497630402124000000}{1801135623563989452} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Tauwehe

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