Question

Find the difference between compound interest and simple interest on \[Rs.45,000 \] at \[12\% \] per annum for \[5 \] years.

Answer 1

Hint: The given question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. We need to know the formulae for finding simple interest. Also, we need to know the formula to find compound interest. We need to know the arithmetic operations with the involvement of power.

Complete step by step solution:
In this question we have,
Principal \[\left( P \right) = Rs.45,000 \]
Interest rate \[\left( R \right) \] \[ = 12\% \] and
Period \[\left( n \right) \] \[ = 5years \]
We know that the formula for finding simple interest is given below,
Simple interest \[ = \dfrac{{P \times R \times T}}{{100}} \to \left( 1 \right) \]
Let’s substitute \[\left( P \right) = Rs.45,000 \] , \[\left( R \right) \] \[ = 12\% \] and \[T = 5 \] in the equation \[\left( 1 \right) \] , we get
Simple interest \[ = \dfrac{{P \times R \times T}}{{100}} \] = \[\dfrac{{45,000 \times 12 \times 5}}{{100}} = Rs.27,000 \]
We know that,
The compound interest \[ = A - P \to \left( 2 \right) \]
Here \[A \to \] is amount
And \[P \to \] is principal
The formula to find the amount \[\left( A \right) \] is shown below,
 \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} \to \left( 3 \right) \]
Let’s substitute \[\left( P \right) = Rs.45,000 \] , \[\left( R \right) \] \[ = 12\% \] and \[n = 5 \] in the above equation, we get
 \[
  A = 45,000{\left( {1 + \dfrac{{12}}{{100}}} \right)^5} = 45,000{\left( {\dfrac{{100 + 12}}{{100}}} \right)^5} = 45,000{\left( {\dfrac{{112}}{{100}}} \right)^5} \\
  A = 45,000{\left( {\dfrac{{28}}{{25}}} \right)^5} \\
  \]
By using a calculator we get
 \[
  A = 45,000 \times 1.76 \\
  A = 79,200 \\
  \]
So, the equation \[\left( 2 \right) \] becomes,
Compound interest \[ = A - P \]
Compound interest \[ = Rs.79200 - Rs.45,000 = Rs.34,200 \]
So, the difference between the simple interest and compound interest,
 \[ = Rs.34,200 - Rs.27,000 = Rs.7,200 \]
So, the final answer is,
The difference between the simple interest and compound interest is equal to \[Rs.7,200 \]

Note: Note that the denominator term would not be equal to zero. Also, remember the formula to find the simple interest and compound interest from the given data in the given question. Also, note that the interest rate is always mentioned in percentage. Note that the mixed fraction can be converted into simple fraction terms by using the formula \[\left( {\dfrac{a}{b} + c} \right) = \dfrac{{a + cb}}{b} \] to make easy calculations. Also, this question describes the arithmetic operations like addition/ subtraction/ multiplication/ division to solve the given question.