Question

A sum of money doubles in $3$ years at compound interest, compounded annually. It will become $4$ times of itself in

• A. $12$ years
• B. $9$ years
• C. $8$ years
• D. $6$ years

Answer 1

The correct option is A $12$ years

Let principal$=p$, rate $\%=R\%$

$t=4$ years

$\therefore$ Amount$=2p$

Case I,

$2P=P{(1+\frac{R}{100})}^4$

$2={(1+\frac{R}{100})}^4$ …..$\left(1\right)$

Case II,

Let after t years it will be $8$ times

$8p=p{(1+\frac{R}{100})}^t$

$2^3={(1+\frac{R}{10})}^t$

By using equation $\left(1\right)$ & $\left(2\right)$

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

By comparing both sides

$t=12$ years.