Question

The amount of Rs. 7500 for 2 years at the rate of 4% per annum compound interest is
A) Rs. 7800
B) Rs. 8100
C) Rs. 8112
D) Rs. 8082

Answer 1

Hint: Here we will directly apply the formula for the amount obtained in compound interest and find its value.

Formula used:
\[{\text{Amount}} = {\text{Principal}}{\left( {{\text{1 + }}\dfrac{{{\text{rate}}}}{{{\text{100}}}}} \right)^{{\text{time}}}}\]
Where principal is the amount of money deposited (principal amount)
Rate is the rate of interest
Time is the time period for which the money is deposited.
Compound interest is mainly used by banks to issue loans and by depositors to keep money at banks.

Complete step by step answer:
Given, Principal value = Rs.7500
Rate of interest =4%
Time period= 2 years

Now since we have to find the value of amount we will apply the formula for amount:
\[
{\text{Amount}} = {\text{Principal}}{\left( {{\text{1 + }}\dfrac{{{\text{rate}}}}{{{\text{100}}}}} \right)^{{\text{time}}}} \\ \]
On substituing the corresponding values, we get
\[ \Rightarrow A = 7500{\left( {1 + \dfrac{4}{{100}}} \right)^2} \\
\Rightarrow A = 7500{\left( {\dfrac{{100 + 4}}{{100}}} \right)^2} \\ \]
On simplification,
\[ \Rightarrow A = 7500\left( {\dfrac{{104}}{{100}} \times \dfrac{{104}}{{100}}} \right) \\
\Rightarrow A = Rs.8112 \\
 \]

Therefore, the amount is Rs 8112. Hence, option C is the correct option.

Note:
The student is likely to make mistake in substituting the value of the rate of interest.
For the formula mentioned above the rate can be taken in percentage only but if we use the following formula:-
\[{\text{Amount}} = {\text{Principal}}{\left( {{\text{1 + rate}}} \right)^{{\text{time}}}}\]
Then the rate of interest should be first converted into decimals.
Students are likely to make mistakes in calculations so they should also take care of calculations to get the correct answer.