The compound interest on Rs. 5000 at 30% p.a. in 3 years :

Options

A. 2480.5
B. 6700
C. 9280.5
D. 3857.5

Answer

To find the compound interest on Rs. 5000 at a rate of 30% per annum over 3 years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 5000
- Rate (r) = 30% per annum
- Time (n) = 3 years

### Step 2: Use the formula for compound interest
The formula to calculate the amount (A) after n years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 5000 \left(1 + \frac{30}{100}\right)^3 \]

### Step 4: Simplify the expression inside the parentheses
\[ A = 5000 \left(1 + 0.30\right)^3 \]
\[ A = 5000 \left(1.30\right)^3 \]

### Step 5: Calculate \( (1.30)^3 \)
Now we calculate \( (1.30)^3 \):
\[ (1.30)^3 = 1.30 \times 1.30 \times 1.30 \]
Calculating step by step:
- \( 1.30 \times 1.30 = 1.69 \)
- \( 1.69 \times 1.30 = 2.197 \)

### Step 6: Substitute back to find the amount
Now substitute back to find A:
\[ A = 5000 \times 2.197 \]
\[ A = 10985 \]

### Step 7: Calculate the compound interest
The compound interest (CI) is given by:
\[ CI = A - P \]
Substituting the values we found:
\[ CI = 10985 - 5000 \]
\[ CI = 5985 \]

### Final Answer
The compound interest on Rs. 5000 at 30% p.a. in 3 years is Rs. 5985.

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