Question

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. Find the simple interest on the same sum for double the time at the rate percent per annum?

Answer 1

Hint: In order to solve the question, first we calculate the principal amount by using the formula of compound interest i.e. \[P{{\left( 1+\dfrac{R}{100} \right)}^{n}}-P\]. Later when we get the principal amount we will need to apply the formula of simple interest i.e. \[\dfrac{P\times R\times T}{100}\] and solve this to get the simple interest. In this way we will get the required answer.

Complete step-by-step solution:
Let the sum be ‘x’.
The formula of compound interest is given by;
Compound interest = \[P{{\left( 1+\dfrac{R}{100} \right)}^{n}}-P\]
Where,
P = principal amount
R = rate of interest
n = no of time i.e. time period
Now,
According to the question,
The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525.
Therefore, using the compound interest formula;
Here,
P = principal amount = x
R = rate of interest = 10%
n = time period = 2 years
\[\Rightarrow x{{\left( 1+\dfrac{10}{100} \right)}^{2}}-x=525\]
Solving the above, we get
\[\Rightarrow x{{\left( \dfrac{11}{10} \right)}^{2}}-x=525\]
\[\Rightarrow \dfrac{121}{100}x-x=525\]
Solving by taking the LCM, we obtained
\[\Rightarrow \dfrac{121x-100x}{100}=525\]
Multiplying both the sides by 100 we get,
\[\Rightarrow 121x-100x=52500\]
\[\Rightarrow 21x=52500\]
Dividing both the sides by 21, we get
\[\Rightarrow x=Rs.2500\]
Therefore, the principal amount is \[Rs.2500\]
Now,
Formula of the simple interest is given by;
Simple interest = \[\dfrac{P\times R\times T}{100}\]
Here,
P = principal amount = Rs. 2500
R = rate of interest given = 5%
T = time period given, = 4 years
Therefore,
Simple interest = \[\dfrac{2500\times 5\times 4}{100}=\dfrac{50000}{100}=Rs.500\]

Therefore, the simple interest on the same sum for double the time at halt the rate of interest is \[Rs.500\].

Note: In order to solve the question, students should remember the formula of calculating a simple interest or compound interest. They should be very careful while doing the calculation part to avoid making any error. Simple interest is the interest that is not compound as the interest is always given only on the principal amount i.e. interest is the same for every year whereas compound interest for each coming year is calculated on amount which is equal to the sum of principal amount and the interest for the previous year.