Question

If the simple interest on a sum at \[4\%\] per annum for 2 years is Rs.80, then the compound interest on the same sum for the same period is?

Answer 1

Hint: In the given question, we are given a simple interest on a sum at \[4\%\] for 2 years and using this information, we have to find the compound interest for the same parameters. We will first find the principal amount using the formula of simple interest, which is, \[S.I=\dfrac{P\times R\times T}{100}\]. Then, after finding the principal amount, we will substitute the value in the formula of compound interest, which is, \[C.I=P\left[ {{\left( 1+\dfrac{R}{100} \right)}^{T}}-1 \right]\]. Hence, we will have compound interest value for the same period.

Complete step by step solution:
According to the given question, we are given the simple interest of a particular amount at the rate of \[4\%\] per annum for 2 years and using this information, we have to find the value of compound interest for the same period.
We will first find the principal amount using the formula of simple interest. We will write the known terms, we have,
We are given rate per annum is, \[R=4\%\]
Time period, \[T=2years\]
And the simple interest is, \[S.I=Rs.80\]
So, the formula of simple interest is, \[S.I=\dfrac{P\times R\times T}{100}\]
Substituting all the known values in the given formula, we get,
\[\Rightarrow 80=\dfrac{P\times 4\times 2}{100}\]
Solving the above expression further, we get,
\[\Rightarrow 80=\dfrac{P\times 8}{100}\]
Writing the above expression in terms of P, we get,
\[\Rightarrow P=\dfrac{80\times 100}{8}\]
\[\Rightarrow P=Rs.1000\]
So, the principal amount is Rs.1000.
We are asked to find the compound interest for the same period. The formula of compound interest is,
\[C.I=P\left[ {{\left( 1+\dfrac{R}{100} \right)}^{T}}-1 \right]\]
Substituting the known values in the formula above, we get,
\[\Rightarrow C.I=1000\left[ {{\left( 1+\dfrac{4}{100} \right)}^{2}}-1 \right]\]
Solving the above expression, we have,
\[\Rightarrow C.I=1000\left[ {{\left( 1+0.04 \right)}^{2}}-1 \right]\]
Adding up the terms in the bracket, we get,
\[\Rightarrow C.I=1000\left[ {{\left( 1.04 \right)}^{2}}-1 \right]\]
\[\Rightarrow C.I=1000\left[ \left( 1.0816 \right)-1 \right]\]
\[\Rightarrow C.I=1000\left[ 0.0816 \right]\]
We get the compound interest as,
\[\Rightarrow C.I=Rs.81.6\]
Therefore, the compound interest for the same period is \[Rs.81.6\]

Note: The simple interest and the compound interest are two different attributes and should not be confused with each other. In simple interest, the interest is not added to the principal amount while calculating the interest while in case of compound interest the interest is added to the principal amount to calculate the amount.