Question

At compound interest rate if a certain sum of money doubles in n years then the amount will be four-fold in ______.

• A. $4n$ years
• B. $2n$ years
• C. $2n^2$ years
• D. $n^2$ years

Answer 1

The correct option is B

$2n$ years

Let principal = ₹x and rate = R
According to question,
$x{(1+\frac{R}{100})}^n=2x$ -------(i)
$\Rightarrow {(1+\frac{R}{100})}^n=2$-------(ii)
Let it become 4 folds in N years.

$x{(1+\frac{R}{100})}^N=4x$

$x{(1+\frac{R}{100})}^N=2\times 2x$

Substitutuing the value of 2 and 2x from (i) and (ii) we get

$x{(1+\frac{R}{100})}^N=\left[\right(1+\frac{R}{100}{)}^n$][$x(1+\frac{R}{100}{)}^n$]

${(1+\frac{R}{100})}^N=(1+\frac{R}{100}{)}^n$$(1+\frac{R}{100}{)}^n$


$\Rightarrow N=2nyears$