Question

The interest on a certain sum of money is \[{\rm{Rs}}1480\] in 2 years and at 10 percent per year. Find the sum of money.

Answer 1

Hint:
Here, we will substitute the given values in the formula for simple interest. Then we will solve it further to find the required sum. Simple Interest is the interest earned on the Principal or the amount of loan.

Formula Used:
We will use the formula \[S.I = \dfrac{{P.R.T}}{{100}}\], where \[P\] is the principal, \[R\] is the rate of interest and \[T\] is the time period.

Complete Step by Step Solution:
Let the certain sum of money or Principal\[ = P\]
It is given that the interest on a certain sum of money is \[{\rm{Rs}}1480\].
Therefore, Simple Interest, \[S.I = 1480\]
Rate of interest per annum, \[R\% = 10\% \]
Time, \[T = 2\] years
We will now calculate the principal using the formula for simple interest.
Multiplying both sides of the formula \[S.I = \dfrac{{P \cdot R \cdot T}}{{100}}\] by 100, we get
\[S.I \times 100 = P \cdot R \cdot T\]
Now, substituting the values, \[T = 2\]years , \[R = 10\] and \[S.I = 1480\]in the above equation, we get,
\[ \Rightarrow 1480 \times 100 = P \cdot \left( {10} \right) \cdot \left( 2 \right)\]
Multiplying the terms, we get
\[ \Rightarrow 14800 = 2P\]
Dividing both sides by 2, we get
\[ \Rightarrow P = 7400\]
Hence, the required sum of money or the Principal, \[ = {\rm{Rs}}7400\]

Therefore, this is the required answer.

Note:
Here, we might make a mistake by thinking the given amount in the question to be principal and then finding out the simple interest on the given amount. This will give us the wrong answer because in the question simple interest is given and not the principal. There is another type of interest, which is the Compound Interest. 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’.