Whakaoti i te 100*(1+5%/12)^12=

$$100 \times ( 1 + \frac { 5 \% } { 12 } ) ^ { 12 } =$$

Aromātai

$$\frac{38388797722185519065061084481}{365203474360565760000000000}\approx 105.116189788$$

Ngā Upane Otinga

Tuhia te \frac{\frac{5}{100}}{12} hei hautanga kotahi.

$$100\left(1+\frac{5}{100\times 12}\right)^{12}$$

Whakareatia te 100 ki te 12, ka 1200.

$$100\left(1+\frac{5}{1200}\right)^{12}$$

Whakahekea te hautanga \frac{5}{1200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$100\left(1+\frac{1}{240}\right)^{12}$$

Tāpirihia te 1 ki te \frac{1}{240}, ka \frac{241}{240}.

$$100\times \left(\frac{241}{240}\right)^{12}$$

Tātaihia te \frac{241}{240} mā te pū o 12, kia riro ko \frac{38388797722185519065061084481}{36520347436056576000000000000}.

$$100\times \frac{38388797722185519065061084481}{36520347436056576000000000000}$$

Whakareatia te 100 ki te \frac{38388797722185519065061084481}{36520347436056576000000000000}, ka \frac{38388797722185519065061084481}{365203474360565760000000000}.

$$\frac{38388797722185519065061084481}{365203474360565760000000000}$$

Tauwehe

$$\frac{241 ^ {12}}{2 ^ {46} \cdot 3 ^ {12} \cdot 5 ^ {10}} = 105\frac{4.243291432611261 \times 10^{25}}{3.6520347436056575 \times 10^{26}} = 105.11618978817332$$