The amount and the compound interest on Rs. 100000 compounded quarterly for 9 months to the rate of 4% per annum is

Options

A. ₹ 103030.10, ₹3030.10
B. ₹ 103300.10, ₹3030.20
C. ₹ 103030.10, ₹ 3031.10
D. ₹ 103300.10, ₹ 3132.20

Answer

To solve the problem of finding the amount and the compound interest on Rs. 100,000 compounded quarterly for 9 months at a rate of 4% per annum, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 100,000
- Rate of interest (r) = 4% per annum = 4/100 = 0.04
- Time (t) = 9 months = 9/12 years = 0.75 years
- Number of times interest is compounded per year (n) = 4 (quarterly)

### Step 2: Use the compound interest formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = Amount after time \( t \)
- \( P \) = Principal amount
- \( r \) = Rate of interest
- \( n \) = Number of times interest is compounded per year
- \( t \) = Time in years

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 100000 \left(1 + \frac{0.04}{4}\right)^{4 \times 0.75} \]

### Step 4: Simplify the expression
Calculate \( \frac{0.04}{4} = 0.01 \), so:
\[ A = 100000 \left(1 + 0.01\right)^{3} \]
\[ A = 100000 \left(1.01\right)^{3} \]

### Step 5: Calculate \( (1.01)^{3} \)
Now, calculate \( (1.01)^{3} \):
\[ (1.01)^{3} = 1.030301 \]

### Step 6: Calculate the amount \( A \)
Now substitute back into the equation for \( A \):
\[ A = 100000 \times 1.030301 = 103030.1 \]

### Step 7: Calculate the compound interest
The compound interest (CI) can be calculated as:
\[ CI = A - P \]
\[ CI = 103030.1 - 100000 = 3030.1 \]

### Final Results
- Amount (A) = Rs. 103030.1
- Compound Interest (CI) = Rs. 3030.1