Whakaoti i te 125=5000(0.01651)(1+0.0165)^t/(1+0.0165)-1

$$125 = \frac { 5000 ( 0.01651 ) ( 1 + 0.0165 ) ^ { t } } { ( 1 + 0.0165 ) - 1 }$$

Whakaoti mō t

$$t=\log_{1.0165}\left(\frac{165}{6604}\right)\approx -225.444882628$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Taupū Kōaro

Whakareatia te 5000 ki te 0.01651, ka 82.55.

$$125=\frac{82.55\left(1+0.0165\right)^{t}}{1+0.0165-1}$$

Tāpirihia te 1 ki te 0.0165, ka 1.0165.

$$125=\frac{82.55\times 1.0165^{t}}{1+0.0165-1}$$

Tāpirihia te 1 ki te 0.0165, ka 1.0165.

$$125=\frac{82.55\times 1.0165^{t}}{1.0165-1}$$

Tangohia te 1 i te 1.0165, ka 0.0165.

$$125=\frac{82.55\times 1.0165^{t}}{0.0165}$$

Whakawehea te 82.55\times 1.0165^{t} ki te 0.0165, kia riro ko \frac{165100}{33}\times 1.0165^{t}.

$$125=\frac{165100}{33}\times 1.0165^{t}$$

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

$$\frac{165100}{33}\times 1.0165^{t}=125$$

Whakawehea ngā taha e rua o te whārite ki te \frac{165100}{33}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$1.0165^{t}=\frac{165}{6604}$$

Tuhia te tau taupū kōaro o ngā taha e rua o te whārite.

$$\log(1.0165^{t})=\log(\frac{165}{6604})$$

Ko te taupū kōaro o tētahi tau ka hīkina ki tētahi pū ko te pū whakarea ki te taupū kōaro o taua tau.

$$t\log(1.0165)=\log(\frac{165}{6604})$$

Whakawehea ngā taha e rua ki te \log(1.0165).

$$t=\frac{\log(\frac{165}{6604})}{\log(1.0165)}$$

Mā te tikanga tātai huri pūtake \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$t=\log_{1.0165}\left(\frac{165}{6604}\right)$$