Whakaoti i te 10,000=xquad(1+0.08/4)^20

$$10,000 = x \quad ( 1 + \frac { 0.08 } { 4 } ) ^ { 20 }$$

Whakaoti mō x

$$x = \frac{95367431640625000000000000000000000000}{14171098670753043575626125424226001} = 6729\frac{1.0108685127771737 \times 10^{34}}{1.4171098670753046 \times 10^{34}} \approx 6729.713331081$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakarohaina te \frac{0.08}{4} mā te whakarea i te taurunga me te tauraro ki te 100.

$$10000=x\left(1+\frac{8}{400}\right)^{20}$$

Whakahekea te hautanga \frac{8}{400} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$10000=x\left(1+\frac{1}{50}\right)^{20}$$

Tāpirihia te 1 ki te \frac{1}{50}, ka \frac{51}{50}.

$$10000=x\times \left(\frac{51}{50}\right)^{20}$$

Tātaihia te \frac{51}{50} mā te pū o 20, kia riro ko \frac{14171098670753043575626125424226001}{9536743164062500000000000000000000}.

$$10000=x\times \frac{14171098670753043575626125424226001}{9536743164062500000000000000000000}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x\times \frac{14171098670753043575626125424226001}{9536743164062500000000000000000000}=10000$$

Me whakarea ngā taha e rua ki te \frac{9536743164062500000000000000000000}{14171098670753043575626125424226001}, te tau utu o \frac{14171098670753043575626125424226001}{9536743164062500000000000000000000}.

$$x=10000\times \frac{9536743164062500000000000000000000}{14171098670753043575626125424226001}$$

Whakareatia te 10000 ki te \frac{9536743164062500000000000000000000}{14171098670753043575626125424226001}, ka \frac{95367431640625000000000000000000000000}{14171098670753043575626125424226001}.

$$x=\frac{95367431640625000000000000000000000000}{14171098670753043575626125424226001}$$