Find the compound interest on Rs. 1000 at 40% per annum compounded quarterly for 1 year.

Options

A. (a) rs 400
B. (b) rs 464
C. (c) rs 464.1
D. (d) rs 500

Answer

To find the compound interest on Rs. 1000 at a rate of 40% per annum compounded quarterly for 1 year, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 1000
- Rate of interest (R) = 40% per annum
- Time (T) = 1 year
- Number of times interest is compounded per year (N) = 4 (quarterly)

### Step 2: Convert the annual interest rate to a quarterly interest rate
The quarterly interest rate can be calculated as:
\[ \text{Quarterly Rate} = \frac{R}{N} = \frac{40}{4} = 10\% \]

### Step 3: Convert the percentage to a decimal for calculations
\[ \text{Quarterly Rate in decimal} = \frac{10}{100} = 0.10 \]

### Step 4: Calculate the total amount after 1 year using the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{N}\right)^{N \cdot T} \]
Substituting the values:
\[ A = 1000 \left(1 + 0.10\right)^{4 \cdot 1} \]
\[ A = 1000 \left(1.10\right)^{4} \]

### Step 5: Calculate \( (1.10)^4 \)
Calculating \( (1.10)^4 \):
\[ (1.10)^4 = 1.4641 \]

### Step 6: Calculate the total amount (A)
Now substitute back to find A:
\[ A = 1000 \times 1.4641 = 1464.10 \]

### Step 7: Calculate the compound interest (CI)
The compound interest can be calculated as:
\[ CI = A - P \]
\[ CI = 1464.10 - 1000 = 464.10 \]

### Final Answer
The compound interest on Rs. 1000 at 40% per annum compounded quarterly for 1 year is Rs. 464.10.

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