CAT 2020 Set-3 | Question: 62

Question

A person invested a certain amount of money at $10\%$ annual interest, compounded half-yearly. After one and a half years, the interest and principal together became $\text{Rs} \; 18522.$ The amount, in rupees, that the person had invested is

Answer 1

We know that, when compound interest is computed half-yearly, time will be $2t$ and rate will be $\dfrac{r}{2}.$

Amount $ = \text{P} \left[ 1 + \left( \dfrac{\dfrac{r}{2}}{100} \right) \right]^{2t}$

$\Rightarrow \boxed{\text{Amount}  = \text{P} \left[ 1 + \dfrac{r}{200} \right]^{2t}}$

Now, $18522 = \text{P} \times \left[ 1 + \dfrac{10}{200} \right]^{2 \times 1.5}$

$\Rightarrow 18522 = \text{P} \times \left[ \dfrac{21}{20}  \right]^{3}$

$\Rightarrow 18522 = \text{P} \left( \dfrac{9261}{8000} \right)$

$\Rightarrow \text{P} =$ ₹ $\; 16000$

$\therefore$ The amount, in rupees, that the person had interested is ₹ $\; 16000.$

Correct Answer $: 16000$