Question

A sum of Rs. 600 amount to Rs. 720 in 4 years. What will be the amount if the rate of interest is increased by 2%.

Answer 1

Hint: To solve this question, we will first find the Simple interest, SI using the formula, SI = amount – principle. And then, we will find the rate of interest using the formula, $SI=\dfrac{PRT}{100}$, where P is the principle amount, R is the rate of interest and T is the time period in years. So, we will get the new rate as 2% + the rate of interest found. And then we will find the value of new SI. Finally, to find the amount when the rate of interest is increased by 2%, we will use the formula, Amount = P + New SI.

Complete step by step solution:
It is given in the question that a sum of Rs. 600 amounts to Rs. 720 in 4 years. And we have been asked to find the amount if the rate of interest is increased by 2%.
So, from this, we can say that the principal amount, P is equal to Rs. 600, the time period is equal to 4 years, the rate of interest is not given and we have also been given the amount at the end of 4 years as, A = Rs. 720.
Now, we know that the simple interest can be calculated by using the formula, Simple interest =Amount – Principal.
That is, SI = A – P……… (i)
So, on substituting the values of A = Rs. 720 and P = Rs. 600 in equation (i), we will get,
SI = 720 – 600
SI = Rs. 120
We also know another formula of simple interest, that is, $SI=\dfrac{PRT}{100}$, where P is the principle amount, R is the rate of interest and T is the time period in years.
So, let us consider $SI=\dfrac{PRT}{100}.........(ii)$.
We will find the value of rate of interest from this formula.
So, on substituting the values of SI = Rs. 120, P = Rs. 600 and T = 4 years in equation (ii), we get,
$120=\dfrac{600\times R\times 4}{100}$
On multiplying both sides of the expression by 100, we will get,
\[\begin{align}
  & 120\times 100=600\times R\times 4 \\
 & 12000=R\times 2400 \\
\end{align}\]
On dividing both the sides by 2400, we get,
$\begin{align}
  & \dfrac{12000}{2400}=R \\
 & R=5 \\
\end{align}$
Hence, we get the rate of interest as 5%.
Now, we have been asked to find the amount when the rate of interest is increased by 2%. So, the rate of interest will become, 5% + 2% = 7%.
So, we know that Amount = P + new SI. So, we will find the new SI. So, we get,
$SI=\dfrac{PRT}{100}=\dfrac{600\times 7\times 4}{100}=Rs.168$
So, we get the new SI as Rs. 168, and we know that P = Rs. 600. So, we will get the amount as,
Amount = P + New SI
Amount = 600 + 168
Amount = Rs. 768.
Hence, we get the amount when the rate of interest is increased by 2% as Rs. 768.

Note: Most of the students make mistake by directly finding the SI using R = 2% as, $SI=\dfrac{600\times 2\times 4}{100}=48$ and then will calculate the final amount as amount = SI + P = 48 + 600 = Rs. 648. Hence, they end up getting the wrong answer, because we are actually asked to find the amount if the rate of interest is increased by 2%. So, 2% is not the initial rate of interest. Hence, the students are advised to read the question properly.