The compound interest on `Rs. 4000` for 4 years at `10%` per annum will be

Options

A. `Rs. 1856.40 `
B. `Rs. 1600 `
C. `Rs. 1856`
D. `Rs. 1756.60`

Answer

To calculate the compound interest on Rs. 4000 for 4 years at an interest rate of 10% per annum, we can follow these steps:

### Step 1: Identify the Principal Amount, Rate, and Time
- Principal (P) = Rs. 4000
- Rate of Interest (R) = 10% per annum
- Time (T) = 4 years

**Hint:** Always start by identifying the given values in the problem.

### Step 2: Convert the Rate of Interest to a Decimal
- To convert the percentage to a decimal, divide by 100.
- R = 10% = 10/100 = 0.10

**Hint:** Remember to convert percentages to decimals when performing calculations.

### Step 3: Use the Compound Interest Formula
The formula for Compound Interest (CI) is:
\[ A = P \left(1 + \frac{R}{n}\right)^{nt} \]
Where:
- A = Amount after time T
- P = Principal amount
- R = Rate of interest (in decimal)
- n = Number of times interest applied per time period (for annual compounding, n = 1)
- t = Time the money is invested for in years

For our case:
- n = 1 (since the interest is compounded annually)

So the formula simplifies to:
\[ A = P (1 + R)^T \]

**Hint:** Familiarize yourself with the compound interest formula and how to apply it.

### Step 4: Substitute the Values into the Formula
Substituting the values we have:
\[ A = 4000 \left(1 + 0.10\right)^4 \]
\[ A = 4000 \left(1.10\right)^4 \]

**Hint:** Make sure to substitute values carefully to avoid mistakes.

### Step 5: Calculate \( (1.10)^4 \)
Now we calculate \( (1.10)^4 \):
\[ (1.10)^4 = 1.4641 \]

**Hint:** Use a calculator for exponentiation if needed.

### Step 6: Calculate the Total Amount (A)
Now substitute back to find A:
\[ A = 4000 \times 1.4641 \]
\[ A = 5856.4 \]

**Hint:** Ensure that you multiply correctly to find the total amount.

### Step 7: Calculate the Compound Interest (CI)
The compound interest is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 5856.4 - 4000 \]
\[ CI = 1856.4 \]

**Hint:** Remember that compound interest is the total amount minus the principal.

### Final Answer
The compound interest on Rs. 4000 for 4 years at 10% per annum is Rs. 1856.4.

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