Question

Vasudevan invested $Rs.60000$ at an interest rate of $12\% $ per annum compounded half yearly. What amount would he get after $1$ year?
A) $Rs.67416$
B) $Rs.78416$
C) $Rs.67786$
D) $Rs.45416$

Answer 1

Hint: The interest is compounded half yearly. So rate is to be taken half the interest per annum. Also there are two half years in a year. Amount after one year depends upon principal, rate of interest and time period.

Formula used: The amount to be paid if the interest is calculated annually is given by,
$A = P{(1 + \dfrac{R}{{100}})^n}$
Where, $P$ is the principal amount, $R$ is the rate of interest and $n$ is the time period.

Complete step-by-step answer:
Given that Vasudevan invested $Rs.60000$ at an interest rate of $12\% $ per annum compounded half yearly.
Let $P$ be the principal amount, $R$ be the rate of interest and $n$ be the time period.
Interest rate is given per annum. But the interest is compounded half yearly.
Therefore the effective interest for half year will be half of that for the full year.
So we have, $Rate,R = \dfrac{{12}}{2} = 6\% $.
Also the time period is two times since there are two half years in a year.
So we have, $n = 2$
Principal is given as $Rs.60000$.
$ \Rightarrow P = 60000$
The amount to be paid if the interest is calculated annually is given by,
$A = P{(1 + \dfrac{R}{{100}})^n}$
Where, $P$ is the principal amount, $R$ is the rate of interest and $n$ is the time period.
Substituting the above values we get,
$A = 60000{(1 + \dfrac{6}{{100}})^2}$
Simplifying we get,
$A = 60000{(\dfrac{{106}}{{100}})^2}$
$ \Rightarrow A = 60000 \times \dfrac{{106 \times 106}}{{100 \times 100}}$
Therefore we get,
$A = 6 \times 106 \times 106 = 67416$
So the amount he would get after one year is $Rs.67416$.

$\therefore $ The answer is option A.

Note: If the interest were compounded annually we can take the time period as one. And also the rate can be taken as the same as the given rate. Anyway, the principal remains constant.
Simple interest is calculated on the principal amount. Compound interest is calculated on the principal amount and also the interest.