Discussion Forum



Each of the questions given below consists of three statements, numbered I, II and II respectively. Please read the question and the statements carefully and decide which of the statement(s) is/are necessary to answer the question.

1)

A sum of money is placed at compound interest. In how many years will it amount to sixteen times of itself ?

I. The sum doubles itself in $4$ years.

II. The sum amounts to eight times of itself in $12$ years.

III. The sum amounts to four times of itself in $8$ years.


A) I only

B) I and II only

C) II and III only

D) I and III only

E) Any one of the three

Answer:

Option E

Explanation:

I. $P\left(1+\frac{R}{100}\right)^{4}$ $=2P$ $\Rightarrow \left(1+\frac{R}{100}\right)^{4}$ $=2$ ---(i)

II. $P\left(1+\frac{R}{100}\right)^{12}$ $=8P$ $\Rightarrow \left(1+\frac{R}{100}\right)^{12}$ $=8$ ---(ii)

III. $P\left(1+\frac{R}{100}\right)^{8}$ $=4P$ $\Rightarrow \left(1+\frac{R}{100}\right)^{8}$ $=4$ ---(iii)

Let the given sum become $16$ times in $n$ years. Then,

$P\left(1+\frac{R}{100}\right)^{n}$ $=16P$

$\Rightarrow \left(1+\frac{R}{100}\right)^{n}$ $=16$ ---(iv)

$\therefore$ Any one of (i), (ii) and (iii) with (iv) will give the value of $n$.

$\therefore$ Correct answer is (E).