Question

A sum of money at compound interest doubles in 4 years. It will amount to eight times itself at the same rate ?

Answer 1

Hint: Use the formula of compound interest to get the first equation with rate ( r ), again use it for the amount which is eight times of the principle to get the other equation . Compare both of them to get to the desired answer.

Complete step-by-step answer:

Let the principle be p , thus the amount becomes 2p in 4 years at the rate of R .
$ \Rightarrow 2p = p{\left( {1 + \dfrac{R}{{100}}} \right)^4}$ ( since the formula for compound interest is $Amount = principle\left( {1 + {{\left( {\dfrac{{Rate}}{{100}}} \right)}^{Time}}} \right)$ )
$ \Rightarrow 2 = {\left( {1 + \dfrac{R}{{100}}} \right)^4}$ - (i)
Let t be the time at which amount becomes eight times , then
$8p = p{\left( {1 + \dfrac{R}{{100}}} \right)^t}$
$ \Rightarrow 8 = {\left( {1 + \dfrac{R}{{100}}} \right)^t}$ - (ii)
Taking cube of equation (i) and comparing with equation (ii) , we get
${\left( {1 + \dfrac{R}{{100}}} \right)^{4 \times 3}} = {\left( {1 + \dfrac{R}{{100}}} \right)^t}$
Therefore , t = $4 \times 3 = 12years$
Amount will become eight times in 12 years .

Note: In such types of questions , we must know and understand the formula for compound interest of a certain principle. Remember to eliminate the unknown rate ( r ) , to get to the desired answer .