The amount of `Rs. 10,000` after 2 years, compounded annually with the rate of interest being `10% `per annum during the first year and `12%` per annum during the second year, would be (In rupees)

Options

A. `Rs. 11,320`
B. `Rs. 12,000`
C. `Rs. 12,320 `
D. `Rs. 12,500`

Answer

To solve the problem of finding the amount after 2 years with compound interest, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Given Values:**
- Principal (P) = Rs. 10,000
- Rate of interest for the first year (R1) = 10%
- Rate of interest for the second year (R2) = 12%

2. **Convert the Rates to Decimal:**
- R1 in decimal = 10/100 = 0.10
- R2 in decimal = 12/100 = 0.12

3. **Calculate the Amount After the First Year:**
- The formula for the amount after the first year (A1) is:
\[ A1 = P \times (1 + R1) \]
- Plugging in the values:
\[ A1 = 10,000 \times (1 + 0.10) = 10,000 \times 1.10 = 11,000 \]

4. **Calculate the Amount After the Second Year:**
- Now, we use the amount from the first year as the principal for the second year.
- The formula for the amount after the second year (A2) is:
\[ A2 = A1 \times (1 + R2) \]
- Plugging in the values:
\[ A2 = 11,000 \times (1 + 0.12) = 11,000 \times 1.12 = 12,320 \]

5. **Final Amount:**
- The total amount after 2 years is Rs. 12,320.

### Final Answer:
The amount after 2 years is **Rs. 12,320**.

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