Find the amount and the compound Interest on Rs 3000 for 2 years at 10% per annum.

Answer

To solve the problem of finding the amount and the compound interest on Rs 3000 for 2 years at 10% per annum, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 3000
- Rate of interest (R) = 10% per annum
- Time (T) = 2 years

### Step 2: Write the formula for the amount (A)
The formula for the amount when compounded annually is:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Now we substitute the values of P, R, and T into the formula:

\[ A = 3000 \left(1 + \frac{10}{100}\right)^2 \]

### Step 4: Simplify the expression inside the brackets
Calculate \(1 + \frac{10}{100}\):

\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]

### Step 5: Raise the result to the power of T (which is 2)
Now we raise \(1.1\) to the power of 2:

\[ (1.1)^2 = 1.1 \times 1.1 = 1.21 \]

### Step 6: Calculate the amount (A)
Now we can calculate the amount:

\[ A = 3000 \times 1.21 = 3630 \]

### Step 7: Calculate the compound interest (CI)
The formula for compound interest is:

\[ CI = A - P \]

Substituting the values we found:

\[ CI = 3630 - 3000 = 630 \]

### Final Answers
- Amount (A) = Rs 3630
- Compound Interest (CI) = Rs 630

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