Whakaoti i te V=V_{0}(1+r/100)^n

$$V = V _ { 0 } ( 1 + \frac { r } { 100 } ) ^ { n }$$

Whakaoti mō V_0 (complex solution)

$$\left\{\begin{matrix}V_{0}=\frac{V}{\left(\frac{r+100}{100}\right)^{n}}\text{, }&n=0\text{ or }r\neq -100\\V_{0}\in \mathrm{C}\text{, }&V=0\text{ and }r=-100\text{ and }n\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$V_{0}\left(1+\frac{r}{100}\right)^{n}=V$$

He hanga arowhānui tō te whārite.

$$\left(\frac{r}{100}+1\right)^{n}V_{0}=V$$

Whakawehea ngā taha e rua ki te \left(1+\frac{1}{100}r\right)^{n}.

$$\frac{\left(\frac{r}{100}+1\right)^{n}V_{0}}{\left(\frac{r}{100}+1\right)^{n}}=\frac{V}{\left(\frac{r}{100}+1\right)^{n}}$$

Mā te whakawehe ki te \left(1+\frac{1}{100}r\right)^{n} ka wetekia te whakareanga ki te \left(1+\frac{1}{100}r\right)^{n}.

$$V_{0}=\frac{V}{\left(\frac{r}{100}+1\right)^{n}}$$

Whakaoti mō V_0

$$\left\{\begin{matrix}V_{0}=\frac{V}{\left(\frac{r+100}{100}\right)^{n}}\text{, }&r>-100\text{ or }\left(Denominator(n)\text{bmod}2=1\text{ and }r<-100\right)\\V_{0}\in \mathrm{R}\text{, }&V=0\text{ and }r=-100\text{ and }n>0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$V_{0}\left(1+\frac{r}{100}\right)^{n}=V$$

He hanga arowhānui tō te whārite.

$$\left(\frac{r}{100}+1\right)^{n}V_{0}=V$$

Whakawehea ngā taha e rua ki te \left(1+\frac{1}{100}r\right)^{n}.

$$\frac{\left(\frac{r}{100}+1\right)^{n}V_{0}}{\left(\frac{r}{100}+1\right)^{n}}=\frac{V}{\left(\frac{r}{100}+1\right)^{n}}$$

Mā te whakawehe ki te \left(1+\frac{1}{100}r\right)^{n} ka wetekia te whakareanga ki te \left(1+\frac{1}{100}r\right)^{n}.

$$V_{0}=\frac{V}{\left(\frac{r}{100}+1\right)^{n}}$$

Whakaoti mō V (complex solution)

$$V=V_{0}\times \left(\frac{r+100}{100}\right)^{n}$$

Whakaoti mō V

$$V=V_{0}\times \left(\frac{r+100}{100}\right)^{n}$$

$$\left(r<-100\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(r=-100\text{ and }n>0\right)\text{ or }r>-100$$