Question

On what principal will the simple interest be $Rs.\,7,008$ in $6$ years $3$ months at $5\%$ per year?

Answer 1

Hint: Here we have been given a simple interest value for which we have to calculate the principal amount for a given time at a given rate. Firstly as the time has to be in years we will convert the months in years as well. Then we will write down the formula for finding simple interest on an amount. Finally we will substitute all the values in the formula and simplify it to get the desired answer.

Complete step by step answer:
We have been given the following information:
Simple Interest $I=Rs.\,7,008$ …..$\left( 1 \right)$
Time $T=6$ Years $3$ months …..$\left( 2 \right)$
As we know $12$ Months $=1$ year
$\Rightarrow 1$ Month $=\dfrac{1}{12}$ year
So as we have to convert $3$ months in year we will multiply by $3$ on both side and get,
$\Rightarrow 3$ Month $=\dfrac{3}{12}$ year
$\Rightarrow 3$ Month $=\dfrac{1}{4}$ years
On substituting the above value in equation (2) we get,
$T=6\times \dfrac{1}{4}$ Years
$\Rightarrow T=\dfrac{25}{4}$ Years …..$\left( 3 \right)$
Rate $R=5\%$ …..$\left( 4 \right)$

Next as we have been given the value of simple interest and we have to find the principal amount we will use the Simple Interest formula.Now the formula for finding the simple Interest is as follows:
Simple Interest $I=\dfrac{P\times R\times T}{100}$
On substituting values from equation (1), (3) and (4) in above formula we get,
$7008=\dfrac{P\times \dfrac{25}{4}\times 5}{100}$
$\Rightarrow 7008\times 100=P\times \dfrac{125}{4}$
Keep $P$ on one side and take the rest value on another as follows:
 $P=\dfrac{7008\times 100\times 4}{125}$
$\therefore P=Rs.\,22,425.60$

On $Rs.\,22,425.60$ the simple interest be $Rs.\,7,008$ in $6$ years $3$ months at $5\%$ per year.

Note: Simple Interest is a method to calculate the interest amount on a principal amount of money for a given time period with the rate specified. It is only applied to the principal amount for the time period given. It is different from the profit as the interest is received by the lender and not the borrower whereas in profit the interest is received by the borrower. It is generally used when we borrow money from a bank.