Question

What is the rate of interest if interest is Rs. 450 for the sum of Rs. 4000 after 2 years?

Answer 1

Hint: The formula of simple interest on a sum of money is given as \[I = \dfrac{{P \times r \times T}}{{100}}\], where $I$ is the simple interest, $P$ is the principal sum, $r$ is the rate of interest per annum and $T$ is the time interval. All values are already given in the question except $r$ i.e. rate of interest. Put these values in the formula and find the value of rate of interest.

Complete step-by-step answer:
According to the question, Rs. 4000 is kept for 2 years and the interest received after this duration is Rs. 450. We have to determine the rate of interest.
We know that the formula to calculate simple interest on a sum of money is given as:
\[ \Rightarrow I = \dfrac{{P \times r \times T}}{{100}}\], where $I$ is the simple interest, $P$ is the principal sum, $r$ is the rate of interest per annum and $T$ is the time interval.
From the data given in the question, we have:
$ \Rightarrow P = 4000,{\text{ }}I = 450{\text{ and }}T = 2{\text{ years}}$
Putting these values in the above formula, we’ll get:
\[450 = \dfrac{{4000 \times r \times 2}}{{100}}\]
Simplifying it further to determine the value of $r$, we’ll get:
\[
   \Rightarrow \dfrac{{450 \times 100}}{{4000 \times 2}} = r \\
   \Rightarrow r = \dfrac{{45}}{8} \\
   \Rightarrow r = 5.625 \\
 \]

Thus the rate of interest for the above scenario is 5.625%.

Additional Information:
The formula used above i.e. \[I = \dfrac{{P \times r \times T}}{{100}}\] is for calculating simple interest only.
If we have to calculate the amount standing in such situations after a period of time then we have to add the simple interest with initial principal sum. This is shown below:
$ \Rightarrow {\text{Amount}} = I + P$

Note:
If the principal sum is subjected to compound interest and not simple interest then the formula to determine amount after a certain period of time is:
$ \Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^T}$