• # question_answer A sum of money placed at compound interest doubles itself in 4 yr. In how many years will it amount to eight times itself? A)  6 yr                              B)  8yr C)  9yr                   D)         12 yr

We have, $P{{\left( 1+\frac{r}{100} \right)}^{4}}=2P$ $\therefore$                  ${{\left( 1+\frac{r}{100} \right)}^{4}}=2$ Cubic on both sides, we get ${{\left( 1+\frac{r}{100} \right)}^{12}}={{2}^{3}}=8$ $\Rightarrow$   $P{{\left( 1+\frac{r}{100} \right)}^{12}}=8P$ Hence, the required time is 12 yr.