Find the compound interest on Rs 4000 for 2 year and 6 months at the rate of 6%?

Options

A. ₹623.932
B. ₹ 232.629
C. ₹ 223.232
D. ₹ 629.232

Answer

To find the compound interest on Rs. 4000 for 2 years and 6 months at the rate of 6%, we will follow these steps:

### Step 1: Convert the time into years
The time given is 2 years and 6 months. We can convert 6 months into years:
\[ \text{Time in years} = 2 + \frac{6}{12} = 2 + 0.5 = 2.5 \text{ years} \]

**Hint:** Remember that 6 months is half a year, so you can convert it by dividing by 12.

### Step 2: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = principal amount (initial investment).
- \(r\) = annual interest rate (in percentage).
- \(n\) = number of years the money is invested or borrowed.

In this case:
- \(P = 4000\)
- \(r = 6\)
- \(n = 2.5\)

**Hint:** Make sure you understand the components of the formula before applying it.

### Step 3: Substitute the values into the formula
Substituting the values into the formula gives:
\[ A = 4000 \left(1 + \frac{6}{100}\right)^{2.5} \]
\[ A = 4000 \left(1 + 0.06\right)^{2.5} \]
\[ A = 4000 \left(1.06\right)^{2.5} \]

**Hint:** Calculate \(1 + \frac{r}{100}\) first to simplify the expression.

### Step 4: Calculate \( (1.06)^{2.5} \)
Using a calculator or exponentiation:
\[ (1.06)^{2.5} \approx 1.148882 \]

**Hint:** If you have a scientific calculator, you can directly compute the power.

### Step 5: Calculate the total amount \(A\)
Now, substituting back:
\[ A \approx 4000 \times 1.148882 \approx 4595.528 \]

**Hint:** Multiply carefully to ensure accuracy.

### Step 6: Calculate the compound interest
To find the compound interest, subtract the principal from the total amount:
\[ \text{Compound Interest} = A - P \]
\[ \text{Compound Interest} = 4595.528 - 4000 \approx 595.528 \]

**Hint:** Always remember to subtract the principal to find the interest earned.

### Final Answer
The compound interest on Rs. 4000 for 2 years and 6 months at the rate of 6% is approximately Rs. 595.53.