Question

What will be the compound interest on a sum of Rs. 25000 after 2 years at the rate of 12 %

• A. 6360
• B. 31360
• C. 6460
• D. 34360

Hint:

For 2 years, the effective interest rate of Compound Interest can be quickly calculated using successive percentage increase: \[ R_{\text{effective}} = x + y + \frac{xy}{100} = 12 + 12 + \frac{144}{100} = 25.44% \] CI $= 25.44% \text{ of } 25000 = 250 \times 25.44 = 6360 \text{ Rs.}$

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods.
Key Formula or Approach:
The compound amount formula is: \[ A = P \left(1 + \frac{R}{100}\right)^n \] where:
- $A$ is the total compound amount.
- $P$ is the principal sum.
- $R$ is the interest rate per annum.
- $n$ is the time period in years.
The Compound Interest (CI) is calculated as: \[ \text{CI} = A - P \]

Step 2: Detailed Explanation:
Given values:
- Principal ($P$) = Rs. $25000$
- Rate ($R$) = $12%$ per annum
- Number of years ($n$) = $2$
Let's substitute these values into the compound amount formula: \[ A = 25000 \left(1 + \frac{12}{100}\right)^2 \] Simplify the fraction inside the parentheses: \[ A = 25000 \left(\frac{112}{100}\right)^2 \] \[ A = 25000 \cdot (1.12)^2 \] Calculate the square of 1.12: \[ 1.12 \times 1.12 = 1.2544 \] Now, multiply by the principal: \[ A = 25000 \cdot 1.2544 \] \[ A = 31360 \text{ Rs.} \] The total accrued amount is Rs. $31360$.
Now, calculate the Compound Interest: \[ \text{CI} = A - P = 31360 - 25000 = 6360 \text{ Rs.} \]

Step 3: Final Answer:
The compound interest is Rs. 6360.