Question

Ashima took a loan of $\mathrm{Rs}.1,00,000$ at $12\%\mathrm{p}.\mathrm{a}.$ compounded half-yearly.

She paid $\mathrm{Rs}.1,12,360$.

If ${(1.06)}^2$ is equal to $1.1236$, then the period for which she took the loan is:

• A. $2\mathrm{years}$
• B. $1\mathrm{year}$
• C. $6\mathrm{months}$
• D. $1\frac{1}{2}\mathrm{years}$

Answer 1

The correct option is B

$1\mathrm{year}$

Explanation for the correct option.
Given, principal, $P=\mathrm{Rs}.100000$
Rate of interest, $R=12\%$ per annum
Amount paid, $A=\mathrm{Rs}.112360$
As, amount is interested compounded half- yearly the formula is,
$A=P{\left(1+\frac{R}{200}\right)}^{2n}$, where $n$ is the time period.

Now by using this formula,
$$\begin{gathered} 112360=100000{\left(1+\frac{12}{200}\right)}^{2n} \\ \Rightarrow \frac{112360}{100000}={\left(1+\frac{12}{200}\right)}^{2n} \\ \Rightarrow {\left(1.12\right)}^1={\left(1.06\right)}^{2n} \\ \Rightarrow {\left(1.12\right)}^1={\left(1.{06}^2\right)}^n \\ \Rightarrow {\left(1.12\right)}^1={\left(1.12\right)}^n \end{gathered}$$

Comparing both of the above equation,

$n=1$
Therefore the time period is $1$ year.

Hence, the correct option is (B).