Question

The compound interest on a certain sum invested for 2 years at 5% per annum is Rs. 328. What will be the simple interest on it at the same rate and for the same time?

Answer 1

Hint: We will need principal amount to calculate the simple interest. Let the principal amount be $x$. Substitute the given value in the formula of the compound interest $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$, where $A$ is the amount, $P$ is the principal amount, $r$ is the rate of interest and $t$ is the time to find the value of $x$. Next, use the formula of simple interest $I = \dfrac{{PRT}}{{100}}$, where $P$ is the principal amount, $R$ is the rate of the interest and $T$ is the time to find the value of simple interest.

Complete step by step Answer:

We are given that the compound interest is Rs. 328 at a rate of interest 5% for 2 years.
We will first have to calculate the principal amount on which interest was calculated.
Let the principal amount on which compound interest was calculated as $x$
And we know that the amount will be $x + 328$, which is the sum of compound interest and principal amount.
Also, the principal amount is calculated as $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$, where $A$ is the amount, $P$ is the principal amount, $r$ is the rate of interest and $t$ is the time.
On substituting the given values, we get,
$x + 328 = x{\left( {1 + \dfrac{5}{{100}}} \right)^2}$
On solving the above equation, we will get,
$
  x + 328 = x{\left( {1 + 0.05} \right)^2} \\
   \Rightarrow x + 328 = x{\left( {1.05} \right)^2} \\
   \Rightarrow 328 = 0.1025x \\
   \Rightarrow x = \dfrac{{328}}{{0.1025}} \\
   \Rightarrow x = 3200 \\
$
Therefore, the principal amount is Rs.3200
But, we have to calculate the simple interest
The formula for calculating the simple interest is $I = \dfrac{{PRT}}{{100}}$, where $P$ is the principal amount, $R$ is the rate of the interest and $T$ is the time.
Then, simple interest is $\dfrac{{3200 \times 5 \times 2}}{{100}} = 320$
Hence, the interest is Rs. 320.

Note: When we calculate compound interest, the principal amount is not the same for every year. It changes as the interest also gets added to it. The total amount is the sum of interest and the principal amount. Many students make mistakes in writing the amount as interest in the formula for compound interest. We can later calculate interest by subtracting the principal amount from the total amount.