The compound interest on Rs. 20,480 at `6(1)/(4)` % per annum for 2 years 73 days is:

Options

A. Rs. 2929
B. Rs. 3000
C. Rs. 3131
D. Rs. 363

Answer

To find the compound interest on Rs. 20,480 at an interest rate of 6.25% per annum for 2 years and 73 days, we can follow these steps:

### Step 1: Convert the time period into years
The total time period is 2 years and 73 days. We need to convert the 73 days into years.

\[ \text{Days in a year} = 365 \]
\[ \text{Years from days} = \frac{73}{365} \approx 0.2 \text{ years} \quad (\text{after simplifying}) \]

So, the total time in years is:

\[ 2 + \frac{73}{365} \approx 2 + 0.2 = 2.2 \text{ years} \]

### Step 2: Convert the interest rate into a decimal
The interest rate is given as 6.25%. We can convert this percentage into a decimal for calculations.

\[ \text{Rate} = \frac{6.25}{100} = 0.0625 \]

### Step 3: Calculate the compound interest using the formula
The formula for compound interest is:

\[ A = P \left(1 + r\right)^n \]

Where:
- \(A\) = Amount after time \(n\)
- \(P\) = Principal amount (Rs. 20,480)
- \(r\) = Rate of interest (0.0625)
- \(n\) = Time in years (2.2)

Substituting the values into the formula:

\[ A = 20480 \left(1 + 0.0625\right)^{2.2} \]

Calculating \(1 + 0.0625\):

\[ 1 + 0.0625 = 1.0625 \]

Now, we calculate \(1.0625^{2.2}\):

\[ A \approx 20480 \times 1.148882 \quad (\text{using a calculator}) \]

Calculating the amount:

\[ A \approx 23,485.34 \]

### Step 4: Calculate the compound interest
Now, we can find the compound interest by subtracting the principal from the total amount:

\[ \text{Compound Interest} = A - P \]
\[ \text{Compound Interest} = 23,485.34 - 20,480 = 3,005.34 \]

### Final Answer
The compound interest on Rs. 20,480 at 6.25% per annum for 2 years and 73 days is approximately Rs. 3,005.34.

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