Find the compound interest on Rs. 4000 at 24% per annum for 3 months, compounded monthly

Answer

To find the compound interest on Rs. 4000 at 24% per annum for 3 months, compounded monthly, we can follow these steps:

### Step 1: Identify the principal amount, rate of interest, and time period
- **Principal (P)** = Rs. 4000
- **Rate of interest (R)** = 24% per annum
- **Time (T)** = 3 months

### Step 2: Convert the annual interest rate to a monthly interest rate
Since the interest is compounded monthly, we need to divide the annual interest rate by 12:
\[ R_{\text{monthly}} = \frac{24\%}{12} = 2\% \]

### Step 3: Convert the time period from months to years
Since we are calculating for 3 months, we convert this to years:
\[ T_{\text{years}} = \frac{3}{12} = \frac{1}{4} \text{ years} \]

### Step 4: Calculate the compound interest using the formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \(A\) = Amount after time \(T\)
- \(P\) = Principal amount
- \(R\) = Rate of interest per period
- \(n\) = Number of periods

Here, \(n\) is the number of months, which is 3.

Substituting the values:
\[ A = 4000 \left(1 + \frac{2}{100}\right)^3 \]
\[ A = 4000 \left(1 + 0.02\right)^3 \]
\[ A = 4000 \left(1.02\right)^3 \]

### Step 5: Calculate \( (1.02)^3 \)
Calculating \( (1.02)^3 \):
\[ (1.02)^3 = 1.061208 \]

### Step 6: Calculate the total amount
Now substitute back into the amount formula:
\[ A = 4000 \times 1.061208 \]
\[ A \approx 4244.83 \]

### Step 7: Calculate the compound interest
The compound interest (CI) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 4244.83 - 4000 \]
\[ CI \approx 244.83 \]

### Final Answer
The compound interest on Rs. 4000 at 24% per annum for 3 months, compounded monthly, is approximately Rs. 244.83.

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