Question

Find the simple interest on \[{\rm{Rs}}{\rm{. 6500}}\] at $8\% $ from 5 January 2015 to 19 March 2015.

Answer 1

Hint: To find the simple interest, we will use the expression of simple interest in terms of principal, rate of interest. We will substitute principal, rate of interest, and the time period in the expression to get simple interest. The time period given in the question is given between particular dates. We will need to convert these days in terms of years.
Formula used:
We can write the expression for simple interest as:
$S.I. = \dfrac{{P \times R \times T}}{{100}}$
Where $P$ is principal, $R$ is rate of interest and $T$ is time period.

Complete step-by-step answer:
Principal for the given is $P = {\rm{Rs}}{\rm{. 6500}}$
The rate of interest is $R = 8\% $ .
 Since it is given we need to calculate simple interest from$8\% $ 5 January 2015 to 19 March 2015, we will need to find the time period for which we need to find the simple interest. From 5 January 2015 to 19 March 2015, there are 73 days. We will convert days into years as expressed:
$\begin{array}{l}
T = \left( {\dfrac{{{\rm{73}}\;{\rm{days}}}}{{{\rm{365}}\;{\rm{days}}}}} \right){\rm{year}}\\
T = \dfrac{{73}}{{365}}\;{\rm{year}}
\end{array}$
We know that the simple interest can be expressed as:
$S.I. = \dfrac{{P \times R \times T}}{{100}}$
 We will substitute ${\rm{Rs}}{\rm{. 6500}}$ for $P$ , $8\% $ for $R$ and $\dfrac{{73}}{{365}}\;{\rm{year}}$ for $T$ in the above expression.
\[\begin{array}{l}
S.I. = \dfrac{{{\rm{Rs}}{\rm{. 6500}} \times 8\% \times \dfrac{{73}}{{365}}\;{\rm{year}}}}{{100}}\\
S.I. = {\rm{Rs}}{\rm{.}}\;\left( {65 \times 8 \times \dfrac{{73}}{{365}}\;} \right)\\
S.I. = {\rm{Rs}}{\rm{.}}\;104
\end{array}\]
Hence the simple interest will be ${\rm{Rs}}{\rm{.}}\;{\rm{104}}$ .

Note: The key point to solve this problem is to find the time period. We need to decode from the question that we need to find the number of days between the dates given. Then, we will divide the number of days by 365 days to find the time period in terms of years. Sometimes a time period is given in terms of months; then, we can divide the number of months by 12 to find the time period in terms of a year.