Question

Calculate the interest on \[{\rm{Rs}}4500\] for \[2\dfrac{1}{2}\] years at \[7\dfrac{2}{3}\% \] per annum is

Answer 1

Hint:
Here, we have to find the simple interest. We will substitute the given values in the formula of simple interest. We will then simplify the expression further to get the required interest. Simple Interest is the interest earned on the Principal or the amount of loan at a certain rate for a particular period of time.

Formula Used:
\[S.I = \dfrac{{P.R.T}}{{100}}\], where \[S.I\] is the Simple Interest, \[P\] is the Principal, \[R\] is the rate of interest per annum and \[T\] is the time period.

Complete step by step solution:
According to the question, the given sum of money or Principal, \[P = {\rm{Rs}}4500\]
The amount is invested for a total duration of \[2\dfrac{1}{2}\] years, so, \[T = 2\dfrac{1}{2} = \dfrac{5}{2}\] years
The rate of interest per annum, \[R = 7\dfrac{2}{3}\% = \dfrac{{23}}{3}\% \]
The principal invested is on simple interest, so we will use the formula of simple interest.
Hence, substituting the given values in this formula \[S.I = \dfrac{{P.R.T}}{{100}}\], we get,
\[S.I = \dfrac{{\left( {4500} \right)\left( {\dfrac{{23}}{3}} \right)\left( {\dfrac{5}{2}} \right)}}{{100}}\]
Dividing the numerator by 100, we get
\[ \Rightarrow S.I = \left( {45} \right) \times \left( {\dfrac{{23}}{3}} \right) \times \left( {\dfrac{5}{2}} \right)\]
Dividing 45 by 3, we get
\[ \Rightarrow S.I = 15 \times 23 \times \left( {\dfrac{5}{2}} \right)\]
Multiplying the terms, we get
\[ \Rightarrow S.I = \dfrac{{1725}}{2}\]
Dividing 1725 by 2, we get
\[ \Rightarrow S.I = {\rm{Rs}}862.5\]

Therefore, the required interest o is \[{\rm{Rs}}862.5\].
Hence, this is the required answer.

Note:
Simple interest is a term used in the banking and finance sector. Here, we should not get confused between simple interest and compound interest. Compound Interest is calculated both on the Principal as well as on the accumulated interest of the previous year, whereas simple interest is based on principal only. Compound interest is also known as ‘interest on interest’. If it is not mentioned to calculate compound interest, then we will calculate simple interest only.