Question

If a deposit of $Rs10000$ amount to $Rs13000$ in $3$ years, what is the rate of simple interest? Calculate the simple interest at the same rate on a deposit of $Rs\,7000$ for two years.

Answer 1

Hint: The problem can be solved easily with the concept of simple interest. Interest is the amount of money gained on the principal over a certain period of time. We should remember the formula for calculations of simple interest as $Interest = \dfrac{{P \times R \times T}}{{100}}$. We substitute the values of given quantities into the formula and then use the method of transposition to calculate the rate of interest.

Complete step-by-step solution:
In the given problem,
Principal $ = P = Rs\,10,000$
Rate of interest $ = R$$\% $
Time Duration $ = 3\,years$
Amount $ = A = Rs\,13,000$
Now, we know that amount is the sum of the simple interest and the principal amount as $Amount = Interest + Principal$.
Substituting the values of amount and principal amount, we get,
$ \Rightarrow 13000 = Interest + 10000$
Shifting the terms and calculating the value of simple interest, we get,
$ \Rightarrow Interest = 13000 - 10000$
$ \Rightarrow Interest = 3000$
So, we have the simple interest as $Rs3000$.
Now, we know the formula for the calculation of simple interest as $Simple\,Interest = \dfrac{{P \times R \times T}}{{100}}$.
So, substituting the values of the known quantities, we get,
$ \Rightarrow Rs\,3000 = \dfrac{{Rs10000 \times R \times 3}}{{100}}$
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow 300R = 3000$
Now, we need to calculate the value of rate of interest using the equation above. So, isolating the only unknown quantity in the equation R, we get,
$ \Rightarrow R = \dfrac{{3000}}{{300}}$
Carrying out the calculations, we get,
$ \Rightarrow R = 10\% $
So, the rate of interest is $10\% $.
Now, we have to calculate the simple interest over the deposit of $Rs\,7000$ on the same rate of interest for two years.
Now, we again use the formula $Simple\,Interest = \dfrac{{P \times R \times T}}{{100}}$ to calculate the simple interest.
So, substituting the values of Principal, rate of interest and time period, we get,
$Simple\,Interest = \dfrac{{Rs\,7000 \times 10 \times 2}}{{100}}$
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow Simple\,Interest = Rs\,70 \times 10 \times 2$
Computing the calculations, we get,
$ \Rightarrow Simple\,Interest = Rs\,1400$
Hence, the simple interest at the same rate on a deposit of $Rs\,7000$ for two years is $Rs\,1400$.

Note: Simple interest is very easy to calculate when we are given the principal amount, the time duration for which the loan is taken and the rate of interest charged by the institution which in this case is the bank. We must take care of the calculations to be sure of the final answer.