Question

Find the compound interest on ₹5000 at 10% per annum for 2 years.

• A. ₹1000
• B. ₹1050
• C. ₹1100
• D. ₹1200

Hint:

For 2 years, you can use the shortcut: $CI = 2 \times (\text{Simple Interest of 1st year}) + (\text{Interest on 1st year's interest})$. Here: $10%$ of $5000$ is $500$. So, $2 \times 500 + (10% \text{ of } 500) = 1000 + 50 = 1050$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Compound interest is calculated on the principal amount as well as the interest accumulated from previous periods. It differs from simple interest, where interest is only calculated on the initial principal.

Step 2: Key Formula or Approach:
The formula for the Amount ($A$) is: \[ A = P \left(1 + \frac{r}{100}\right)^n \] The Compound Interest ($CI$) is then found by: \[ CI = A - P \] Given: $P = 5000$, $r = 10$, $n = 2$.

Step 3: Calculation:
1. Find the Amount ($A$): \[ A = 5000 \left(1 + \frac{10}{100}\right)^2 = 5000 (1.1)^2 \] \[ A = 5000 \times 1.21 = 6050 \] 2. Find the Interest ($CI$): \[ CI = 6050 - 5000 = 1050 \]

Step 4: Final Answer:
The compound interest is ₹1050.