Question

At the rate of $10\%$ per annum compounded quarterly, how long would it take for a sum of Rs. $10000$ to compound to Rs. $20736$.

• A. $1$ year
• B. $2$ years
• C. $3$ years
• D. $4$ years

Answer 1

Answer: (D)

$4$ years

Let the time be $n$ years.
Given, $P=$ Rs. $10000,r=15\%$ and $A=$ Rs. $20736$
We know the formula,
$A=P{(1+\frac{r}{100})}^n$
$\Rightarrow 20736=10000{(1+\frac{10}{100})}^n$
$\Rightarrow \frac{20736}{10000}={\left(\frac{110}{100}\right)}^n$
$\Rightarrow {\left(\frac{12}{10}\right)}^4={\left(\frac{11}{10}\right)}^n$
$\Rightarrow n=4$
Therefore, in $4$ years Rs. $10000$ will become Rs. $20736$ at $10\%$ per annum compounded quarterly.