Question

Calculate the amount and compound interest, if principal is Rs.1500, rate is 2% (per six month) and compounded semiannually.
\[\begin{align}
  & \text{A}.\text{ 6}00 \\
 & \text{B}.\text{ 62}0 \\
 & \text{C}.\text{ 64}0 \\
 & \text{D}.\text{ 66}0 \\
\end{align}\]

Answer 1

Hint: According to the question, we are given that, the principal is 1500. So, we have P=1500. Rate is 2% so $r=\dfrac{2}{100}$ then as we have interest in semiannually (per six months) so the number of periods in a year is $\dfrac{12}{6}=2$ so we have n as 2.
Then we use formula $A=P{{\left( 1+r \right)}^{n}}$ to find the amount. Once we have the amount, we use $I=A-P$ to find the compound interest (I).

Complete step by step answer:
We are given that, the principal is Rs.1500, the rate per six months as 2%. We are asked to find the amount and compound interest.
We are given the principal as of 1500. So we have P=1500
Now rate is 2% per six month. So, we have $r=2%=\dfrac{2}{100}$
As we know, the rate is for 6 months. So, in one year there will be $6+6=12$
Two periods of six months each. So we get n as 2 $\Rightarrow n=2$
We are asked to find the amount. We know the amount (A) is given as:
\[A=P{{\left( 1+r \right)}^{n}}\]
As we have P = 1500, $r=\dfrac{2}{100}$ and n = 2. So,
\[A=1500{{\left( 1+\dfrac{2}{100} \right)}^{2}}\]
Simplifying we get:
\[A=1500{{\left( 1.2 \right)}^{2}}\]
Solving further we get:
\[A=2160\]
Now, we know that amount is nothing but the sum of the principal and the compound interest (I). So from here, we get.
Compound interest is given as \[I=A-P\] as we have A = 2160 and P = 1500. So, we get:
\[\begin{align}
  & I=2160-1500 \\
 & \Rightarrow 660 \\
\end{align}\]
So, we get our compound interest as 660. Hence, option D is the correct answer.


Note:
 While solving such questions, we have to be careful about how the interest rate is applied and according to the same, we get our number of periods.
If the rate is annual then the number of periods in a year is 1.
If the rate is monthly then the number of periods in a year is 12.
If the rate is semiannual then the number of periods in a year is 2.
If the rate is quarterly, then the number of periods in a year is 4.