Question

A man invests ₨\[46,875\] at \[4\% \] per annum compound interest for \[3\] years. Calculate:
I. The interested in the first year.
II.The amount standing to his credit at the end of the second year.
III.The interest for the third year.

Answer 1

Hint: Here, in the given question, we have been asked to find the compound interest given the initial principal amount, rate of interest and time period. We will simply use the formula of compound interest. But remember, compound interest formula gives us the final amount i.e. principal amount plus the interest earned for the period. To calculate only the interest, we will subtract the principal amount.
Formula used:
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}\], where
\[A\] = total amount (principal plus interest)
\[P\] = Principal amount
\[R\] = Rate of interest
\[N\] = time (in years)

Complete step-by-step answer:
I.Given: Principal Amount \[\left( P \right)\] = ₨\[46,875\]
Rate of interest \[\left( R \right) = 4\% p.a.\]
To calculate: interest for the first year
We have \[P = 46875\], \[R = 4\% \], \[N = 1\]
Using compound interest formula which is given by \[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}\]
\[
  A = 46,875{\left( {1 + \dfrac{4}{{100}}} \right)^1} \\
   \Rightarrow A = 46,875\left( {\dfrac{{104}}{{100}}} \right) \\
   \Rightarrow A = 48750 \;
 \]
We get the total amount after first year as ₨\[48750\].
Interest for first year = Total amount – Principal
\[
   = 48750 - 46875 \\
   = 1875 \;
 \]

II.To calculate: the amount standing to his credit at the end of the second year
We have \[P = 46875\], \[R = 4\% \], \[N = 2\], Therefore,
\[
  A = 46875{\left( {1 + \dfrac{4}{{100}}} \right)^2} \\
  A = 46875{\left( {\dfrac{{104}}{{100}}} \right)^2} \\
  A = 50700 \;
 \]

III.To calculate: the interest for the third year
We have \[P = 46875\], \[R = 4\% \], \[N = 3\], Therefore,
\[
  A = 46875{\left( {1 + \dfrac{4}{{100}}} \right)^3} \\
  A = 46875{\left( {\dfrac{{104}}{{100}}} \right)^3} \\
  A = 52728 \;
 \]
We get the total amount after three year as ₨\[52728\].
Interest for third year = Total amount – Principal
\[
   = 52728 - 50700 \\
   = 2028 \;
 \]
I.₨\[1,875\]
II.₨\[50,700\]
III.₨\[2,028\]

Note: We should understand that the compound interest for the first year is the same as the simple interest for the first year. We could simply use a simple interest formula to calculate the first year of interest which is given as \[S.I. = \dfrac{{PRT}}{{100}}\], where \[P,R,T\] denotes principal amount, rate of interest and time in years respectively.