Question

To what sum will ₹6000 accumulate in 8 years if invested at an effective rate of $8\% $?
A) ₹ $11105.40$
B) ₹ 11000
C) ₹ $10105.40$
D) ₹ $11005.40$

Answer 1

Hint: Here, we will have to find the amount. We will use the amount formula if it is compounded annually to find the amount by substituting the principal, rate of interest and the number of years. Compound interest is defined as the interest calculated for the principal and the interest accumulated over a period of years before.

Formula used:
If the amount is compounded annually, then the amount is given by $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$ where $A$ is the amount, $P$ is the principal, $R$ is the rate of Interest and $t$ is the number of years.

Complete step by step solution:
We are given that the sum ₹6000 will accumulate in 8 years if invested at an effective rate of \[8\%\].
Here, the interest is accumulated to the sum, so the interest would be a Compound Interest.
Substituting \[P = 6000\], \[R = 8\% \] and $t = 8$ in the formula $A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$, we get
By using the compound interest formula, we get
$ \Rightarrow A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$
$A = 6000{\left( {1 + \dfrac{8}{{100}}} \right)^8}$
By taking LCM inside the bracket, we get
$ \Rightarrow A = 6000{\left( {1 \times \dfrac{{100}}{{100}} + \dfrac{8}{{100}}} \right)^8}$
$ \Rightarrow A = 6000{\left( {\dfrac{{100 + 8}}{{100}}} \right)^8}$
Adding the terms, we get
$ \Rightarrow A = 6000{\left( {\dfrac{{54}}{{50}}} \right)^8}$
Simplifying the expression, we get
$ \Rightarrow A = 6000 \times 1.8509$
By multiplying the terms, we get
$ \Rightarrow A = {\text{Rs}}.11105.40$
Therefore, the amount will be ₹ $11105.40$.

Thus, option (A) is the correct answer.

Note:
Here, we might get confused between compound interest and simple interest and hence, use the wrong formula. The main difference between simple interest and compound interest is that simple interest is based only on the principal amount whereas compound interest is based on the principal amount and the interest compounded for a period. So, the amount is accumulated on the compound interest. Here, we might make a mistake by calculating principal instead of amount.