Question

a sum of money triple itself in 5 year at compond interest in how many year it will become 81 time of itself​

Answer 1

$\boxed{\sf{A=P(1+\frac{r}{100})^n}}$

$\sf{3P=P(1+\frac{R}{100})^3$

$\sf{Cancelling\:P\:on\:both\:sides\:,$

$\implies\sf{3=(1+\frac{R}{100})^3$

$\sf{Here\:,$

• $\sf{A=81P$

• $\sf{t=?$

$\implies\sf{81P=P(1+\frac{R}{100})^t$

$\sf{Cancelling\:P\:on\:both\:sides\:,$

$\implies\sf{81=(1+\frac{R}{100})^t$

$\implies\sf{3^4=(1+\frac{R}{100})^t$

$\implies\sf{[(1+\frac{R}{100}^3)]^4=(1+\frac{R}{100})^t$

$\implies\sf{(1+\frac{R}{100})^{12}=(1+\frac{R}{100})^t$

$\boxed{\sf{t=6\:Years}}$