Question

Calculate the compound interest for ₹25,000 for 3 years at the rate of 6% per annum compounded annually.
A. 4775.40
B. 4776.40
C. 4660
D. None of these

Answer 1

Hint: Now in this question we have to straightaway calculate the Compound Interest using the formula for the same.

Complete step by step solution:
Now, according to the question we have to find the Compound Interest for a Principal of ₹25000 with the rate of interest as 6% per annum over a period of 3years, when the interest is being calculated annually. So we can say that-
Given,
$
  P = Rs25000 \\
  r = 6\% \\
  n = 3years \\
 $
Now, the formula for Compound Interest, which can also be denoted with CI is given as:
$CI = P\left[ {{{\left( {1 + \dfrac{r}{{100}}} \right)}^n} - 1} \right]$where, CI is the Compound Interest, P is the Principal, r is the rate of interest and n is the number of terms for which the CI is being calculated.
So, putting the values of the respective variables P=25000, r=6% and n=3years from the information given to us,
We will get the CI as:
$CI = 25000\left[ {{{\left( {1 + \dfrac{6}{{100}}} \right)}^3} - 1} \right]$
Which on simplifying will become:
$
  CI = 25000\left[ {{{\left( {1 + \dfrac{6}{{100}}} \right)}^3} - 1} \right] \\
   = 25000\left[ {{{\left( {\dfrac{{100 + 6}}{{100}}} \right)}^3} - 1} \right] \\
   = 25000\left[ {{{\left( {\dfrac{{106}}{{100}}} \right)}^3} - 1} \right] \\
   = 25000\left[ {{{\left( {\dfrac{{53}}{{50}}} \right)}^3} - 1} \right] \\
   = 25000\left[ {\dfrac{{{{\left( {53} \right)}^3} - {{\left( {50} \right)}^3}}}{{{{\left( {50} \right)}^3}}}} \right] \\
 $
Now we will use the formula for expansion for difference of cubes for the numerator which is given as:
${a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)$
So, using this formula, the expression will now simplify into:
$
   = 25000\left[ {\dfrac{{\left( {53 - 50} \right)\left( {{{\left( {53} \right)}^2} + \left( {53} \right)\left( {50} \right) + {{\left( {50} \right)}^2}} \right)}}{{{{\left( {50} \right)}^3}}}} \right] \\
   = 25000\left[ {\dfrac{{3 \times \left( {2809 + 2650 + 2500} \right)}}{{{{\left( {50} \right)}^3}}}} \right] \\
   = 25000\left[ {\dfrac{{3 \times \left( {7959} \right)}}{{50 \times 50 \times 50}}} \right] \\
   = \dfrac{{23877}}{5} \\
   = 4775.4 \\
 $

That is the compound interest comes out to be ₹4775.40

Hence, the correct option is A.

Note: Care must be taken while calculating the value of the Compound Interest, especially with the decimal places.