Question

Find the compound interest on $Rs.6000$ at $10\% $ p.a for $2\dfrac{3}{4}$ years compounded annually.

Answer 1

Hint: Use the formula for Compound interest to solve this question. The formula is $A = P{(1 + \dfrac{r}{n})^{(nt)}}$. Determine the value of the variables from the question and substitute them in the formula to arrive at the total amount. After getting the total amount, subtract the principal amount from it to get the compound interest.

Complete step-by-step answer:
We use the formula of compound interest (CI) to solve this question. The formula is,
$A = P{(1 + \dfrac{r}{n})^{(nt)}}$ , where $A = P + CI$ , that is the total amount including the interest, $P$ is the principal amount, $r$ is the rate of interest per annum, $n$ is the number of times that the interest is compounded per unit time and $t$ is the time period for which the money is invested.
In this question,
$P = Rs.6000$
$r = 10\% $
$t = 2\dfrac{3}{4}years = \dfrac{{11}}{4}years$,and,
$n = 1$ , because it is compounded only once annually.
We will now substitute these values into the above formula.
$
  A = P{(1 + \dfrac{r}{n})^{(nt)}} \\
   \Rightarrow A = 6000{(1 + \dfrac{{10}}{1})^{(1 \times \dfrac{{11}}{4})}} \\
   \Rightarrow A = 6000{(11)^{2.75}} \\
   \Rightarrow A = 6000 \times 730.85 \\
   \Rightarrow A = 4385116.49 \\
 $
So the total amount received after the given time period will be $Rs.4385116.49$
To find the amount of interest in this, we need to subtract the original principal amount from this.
So, Compound Interest= $Rs.4385116.49 - Rs.6000$ $ = Rs.4379116.49$
So the answer is $Rs.4379116.49$.

Note: Be very careful while determining the value of $n$. It depends on the unit of time. So if time had been given in months, it would have been equal to the number of times the interest is compounded in one month. Also, read the question carefully. If the question asks for the amount of compound interest, then it is essential to subtract the Principal amount from the total amount. Do not forget to do that step.