CAT 2020 Slot 3 QA Question 16: 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 Rs 18522. The amount, in rupees, that

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 Rs 18522. The amount, in rupees, that

Accepted Answer

A 10% annual rate compounded half-yearly means 5% per half-year. One and a half years contain 3 half-years.
Let the principal be $P$.
$P(1.05)^3 = 18522$

$\Rightarrow P = \dfrac{18522}{(1.05)^3}$

$\Rightarrow P = \dfrac{18522}{1.157625} = 16000$

Answer: 16000

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 Rs 18522. The amount, in rupees, that the person had invested is