Question

What will be the compound interest on 4000 at 5% per annum in two years.

Answer 1

Hint: Here we are given the principal amount of money, the rate of interest and it is to be compounded annually for 2 years. We will find out the compound interest using the formula. Consider all values given in question and try to identify which one to use where.
\[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\]
This will help in understanding the problem.

Complete step-by-step answer:
Here, we have the principal amount given (P) = 4000Rs.
The rate of interest per annum (r) = 5%
The total duration given is 2 years.
As we know, the formula of compound interest is
 \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\]
A is the total amount. R is rate of interest and P is the principal amount
Compounded for two years.
Given in the question, $ P = 4000Rs,r = 5\% ,n = 2years$
\[
  A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n} \\
   \Rightarrow A = 4000{\left( {1 + \dfrac{5}{{100}}} \right)^2} \\
   \Rightarrow A = 4000{\left( {1 + \dfrac{1}{{20}}} \right)^2} \;
 \]
Further, calculating the fraction we get
\[
   \Rightarrow A = 4000{\left( {\dfrac{{21}}{{20}}} \right)^2} \\
  Squaring\,bracket \\
   \Rightarrow A = 4000\left( {\dfrac{{441}}{{400}}} \right) \\
   \Rightarrow A = 4410Rs. \;
 \]
So, the amount after two years will be
 \[A = 4410Rs.\]
The compound interest will be
$
  Interest = Amount - Principal \\
   \Rightarrow Interest = 4410 - 4000 \\
   \Rightarrow Interest = 410\;Rs. \;
 $
So, the correct answer is “410 Rs.”.

Note: Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest