Question

What would be the Compound interest on Rs.17500 at the rate of 12 percent per annum after 2 years?
A. Rs. 4442
B. Rs. 4452
C. Rs.4462
D. Rs.4482

Answer 1

Hint: We will directly use the formula of Compound Interest to find the C.I in our question. C.I. is given as $\left[ P{{\left( 1+\dfrac{r}{100} \right)}^{T}}-P \right]$ , where $P$ is our principal amount, $T$ is the time period and $r$ is the rate of interest.
Complete step-by-step solution -
It is given in the question that we have to find the compound interest of Rs.17500 at the rate of 12 p.c.p.a. after 2 years. We will first find the total amount and then subtract the principal amount from the total amount to get the compound interest on Rs. 17500 at the rate of 12% in 2 years. We know that the total amount is given by, $A=P{{\left( 1+\dfrac{r}{100} \right)}^{T}}$, where $P$ is the principal amount, $A$ is the total amount, $r$ is the rate of interest and $T$ is the time period. In the question, we have $P$ as Rs. 17500, $r$ as 12 p.c.p.a and time as 2 years. We will first find the amount by substituting these values in the above formula. So, by substituting the given values in the formula, we get, $\begin{align}
  & A=17500{{\left( 1+\dfrac{12}{100} \right)}^{2}} \\
 & =17500{{\left( \dfrac{100+12}{100} \right)}^{2}} \\
 & =\dfrac{17500\times 112\times 112}{100\times 100} \\
 & =21952 \\
\end{align}$
Thus, we get the total amount as Rs. 21952. Now we will calculate the C.I. as (Amount - Principal), C.I. = 21952 - 17500 = Rs. 4452. Hence we get the C.I. as Rs. 4452 and therefore the correct answer is option B.

Note: It is recommended to memorize the direct formula of the total amount for solving problems based on compound interest. If we remember the formula of the total amount and know that C.I. is given as (Amount - Principal), then this is just like any other mathematical operations of multiplication, subtraction, addition, or multiplication.