Question

The C.I. on Rs. 4,000 for 6 months at 12% p.a. payable quarterly is?
(a) Rs. 243.60
(b) Rs. 240
(c) Rs. 243
(d) None of these

Answer 1

Hint: Here, we will apply the formula for the compound interest on any amount. The formula for compound interest to find the total Amount is given as $C.I.=P{{\left( 1+\dfrac{r}{n} \right)}^{tn}}$ . Since, it is given that the interest is payable quarterly, so the value of n will be 4 and the time that we are taking must be in years.

Complete step-by-step answer:
Here, we are given that the principal amount is Rs. 4,000.
The rate of interest is given as 12% per annum.
The time given to us here is 6 months. But to apply the formula for compound interest, the time given must be in years. We know that 12 months make 1 year. So, 6 months will make $\dfrac{1}{2}$ year.
Also, we are given rate percent in this problem, so the formula becomes:
$A=P{{\left( 1+\dfrac{r}{100\times n} \right)}^{n\times t}}...........\left( 1 \right)$
The interest is payable quarterly, so the value of n is 4. On putting the respective values in equation (1), we get:
$\begin{align}
  & A=4000{{\left( 1+\dfrac{12}{100\times 4} \right)}^{4\times \dfrac{1}{2}}} \\
 & \Rightarrow A=4000{{\left( 1+\dfrac{3}{100} \right)}^{2}} \\
 & \Rightarrow A=4000{{\left( 1+0.03 \right)}^{2}} \\
 & \Rightarrow A=4000\times {{\left( 1.03 \right)}^{2}}=4243.6 \\
\end{align}$
So, A = Rs. 4243.6
Here, we have to find the compound interest. Since, interest is given as total amount – principal amount.
So, we have:
Compound interest = Rs. 4243.6 – Rs. 4000 = Rs. 243.6
Hence, option (a) is the correct answer.

Note: The most common mistake that a student may come across here is that they don’t divide the rate by 100. The formula $A=P{{\left( 1+\dfrac{r}{n} \right)}^{n\times t}}$ is applied when the annual rate is given but when the rate percent is given, we have to divide the rate by 100. It should also be kept in mind that for finding the interest, we have to subtract the principal amount from the total amount. Another mistake which may occur is that one does not convert the time given in months to year.