What will be the compound interset on a sum of Rs.1200 for 2 years at the rate of 20% per annum when the interset is compounded yealy ?

Options

A. Rs. 624
B. Rs. 504
C. Rs. 576
D. Rs. 528

Answer

To calculate the compound interest on a sum of Rs.1200 for 2 years at an interest rate of 20% per annum, compounded yearly, we can follow these steps:

### Step 1: Identify the values
- Principal (P) = Rs. 1200
- Rate of interest (R) = 20% per annum
- Time (T) = 2 years

### Step 2: Use the compound interest formula
The formula for compound interest (A) is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- A = Total amount after time T
- P = Principal amount
- R = Rate of interest
- T = Time in years

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ A = 1200 \left(1 + \frac{20}{100}\right)^2 \]
\[ A = 1200 \left(1 + 0.20\right)^2 \]
\[ A = 1200 \left(1.20\right)^2 \]

### Step 4: Calculate \( (1.20)^2 \)
Now, calculate \( (1.20)^2 \):
\[ (1.20)^2 = 1.44 \]

### Step 5: Calculate the total amount (A)
Now substitute back to find A:
\[ A = 1200 \times 1.44 \]
\[ A = 1728 \]

### Step 6: Calculate the compound interest (CI)
Now, to find the compound interest (CI), we subtract the principal from the total amount:
\[ CI = A - P \]
\[ CI = 1728 - 1200 \]
\[ CI = 528 \]

### Final Answer
The compound interest on a sum of Rs.1200 for 2 years at the rate of 20% per annum is Rs. 528.

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