Step 1: Understanding the Concept:
Compound Interest (CI) is the interest calculated on the initial principal and also on the accumulated interest of previous periods.
Unlike simple interest, which is calculated only on the original amount, compound interest results in the principal growing at an increasing rate over time—a phenomenon often called the "power of compounding."
When interest is compounded annually, the interest earned at the end of Year 1 is added to the principal to form the new starting amount for Year 2.
Key Formula or Approach:
1. Total Amount (\(A\)) = \(P \left( 1 + \frac{R}{100} \right)^n\)
2. Compound Interest (\(CI\)) = \(A - P\)
where \(P = 10,000\), \(R = 10\), and \(n = 2\).
Step 2: Detailed Explanation:
Let's solve this using the formula-based method first. Substitute the values into the Amount formula:
\[ A = 10000 \left( 1 + \frac{10}{100} \right)^2 \]
Simplify the fraction inside the bracket:
\[ A = 10000 \left( 1 + \frac{1}{10} \right)^2 = 10000 \left( \frac{11}{10} \right)^2 \]
Calculate the square of 11/10:
\[ \frac{11 \times 11}{10 \times 10} = \frac{121}{100} \]
Now, calculate the total amount:
\[ A = 10000 \times \frac{121}{100} \]
Cancel the zeros:
\[ A = 100 \times 121 = 12,100 \]
The Compound Interest is the difference between this amount and the original principal:
\[ CI = 12,100 - 10,000 = 2,100 \]
Alternatively, we can use the "Step" method:
Interest for Year 1: \(10% \text{ of } 10,000 = 1,000\).
Interest for Year 2: \(10% \text{ of (10,000 + 1,000)} = 10% \text{ of } 11,000 = 1,100\).
Total CI = \(1,000 + 1,100 = 2,100\).
Step 3: Final Answer:
The total compound interest earned is 2,100. Thus, Option (B) is the correct choice.