Question

Mr Jane donates Rs. 1 lakh to a school and the interest on it is to be used for awarding five scholarships of equal value. If the value of each scholarship is Rs 1,500, find the rate of interest.

Answer 1

Hint:
Here, we are required to find the rate of interest. We will first find the value of 5 scholarships by multiplying 5 the value of each scholarship. We will use the information given in the question to find the simple interest. Then we will use the formula of simple Interest and substitute all the given values to find the required rate of interest per annum.

Formula Used:
We will use the formula of simple interest, \[S.I = \dfrac{{P.R.T}}{{100}}\], 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:
We know that Mr Jane donated Rs. 1 lakh to a school. Hence, the Principal,\[P = {\rm{Rs}}1,00,000\]
Also, the value of each scholarship is Rs 1,500. Therefore, the value of 5 scholarships\[ = 5 \times {\rm{Rs}}1500 = {\rm{Rs}}.7500\]. Now, it is given that the interest on the principle will be used for awarding five scholarships of equal value. Hence, Simple Interest, \[S.I = \] Value of 5 scholarships
\[ \Rightarrow S.I = {\rm{Rs}}7500\]
We know that,
Rate of interest per annum \[ = R\% \]
Time Period, \[T = 1\] year
We will now find the rate of interest using the formula \[S.I = \dfrac{{P.R.T}}{{100}}\].
Multiplying both sides by 100, we get
\[S.I \times 100 = P.R.T\]
Now, substituting the values \[P = 1,00,000\], \[T = 1\] year and \[S.I = {\rm{Rs}}7500\] in the above equation, we get,
\[ \Rightarrow 7500 \times 100 = \left( {100000} \right) \cdot R \cdot \left( 1 \right)\]
Multiplying the terms, we get
\[ \Rightarrow 750000 = \left( {100000} \right) \cdot R\]
Dividing both sides by 1,00,000, we get
\[ \Rightarrow \dfrac{{75}}{{10}} = R\]
Dividing 75 by 10, we get
\[ \Rightarrow R = 7.5\% \]
Hence, Rate of interest, \[R = 7.5\% \]

Therefore, the required rate of interest when the interest is used for awarding five scholarships of equal value is \[7.5\% \].

Note:
We might get confused between simple interest and compound interest and might use the formula of compound Interest. Simple Interest is the interest earned on the Principal or the amount of loan. Compound Interest is calculated both on the Principal as well as on the accumulated interest of the previous year. Hence, this is also known as ‘interest on interest’.
Its formula is:
\[C.I = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} - P\], where, \[C.I\] is the Compound Interest, \[P\] is the Principal, \[R\] is the rate of interest per annum and \[n\] is the time period.