What is the compound interest (in Rs.) on Rs. 12500 at the rate of 12% per annum compounded yearly for 2 years?

Options

A. 3000
B. `2980`
C. `3050 `
D. `3180`

Answer

To calculate the compound interest on Rs. 12,500 at a rate of 12% per annum compounded yearly for 2 years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 12,500
- Rate of interest (R) = 12% per annum
- Time (T) = 2 years

**Hint:** Always start by identifying the principal amount, interest rate, and time period for the calculation.

### Step 2: Convert the rate of interest into a decimal
To use the formula, convert the percentage rate into a decimal:
\[ R = \frac{12}{100} = 0.12 \]

**Hint:** Remember to convert percentage rates into decimals for calculations.

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P(1 + R)^T \]
Where:
- A = Amount after time T
- P = Principal
- R = Rate of interest (in decimal)
- T = Time (in years)

Substituting the values:
\[ A = 12500(1 + 0.12)^2 \]

**Hint:** Make sure to use parentheses correctly to ensure the order of operations is followed.

### Step 4: Calculate the amount (A)
First, calculate \( (1 + R) \):
\[ 1 + 0.12 = 1.12 \]

Now raise it to the power of T (which is 2):
\[ (1.12)^2 = 1.2544 \]

Now calculate A:
\[ A = 12500 \times 1.2544 = 15680 \]

**Hint:** Calculate the power before multiplying by the principal amount.

### Step 5: Calculate the compound interest (CI)
Now, to find the compound interest, subtract the principal from the amount:
\[ CI = A - P \]
\[ CI = 15680 - 12500 = 3180 \]

**Hint:** The compound interest is the total amount minus the principal.

### Final Answer
The compound interest on Rs. 12,500 at the rate of 12% per annum compounded yearly for 2 years is Rs. 3,180.

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