What will be the compound interest on Rs. 15625 for `2(1)/(2)` years at 4% per annum?

Answer

To find the compound interest on Rs. 15625 for 2.5 years at an interest rate of 4% per annum, we can follow these steps:

### Step 1: Identify the principal, rate, and time.
- Principal (P) = Rs. 15625
- Rate (R) = 4% per annum
- Time (T) = 2.5 years

### Step 2: Convert the time into years and calculate the compound interest.
We can use the formula for compound interest:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- A = Amount after time T
- P = Principal
- R = Rate of interest
- T = Time in years

### Step 3: Substitute the values into the formula.
Substituting the values we have:
\[ A = 15625 \left(1 + \frac{4}{100}\right)^{2.5} \]
\[ A = 15625 \left(1 + 0.04\right)^{2.5} \]
\[ A = 15625 \left(1.04\right)^{2.5} \]

### Step 4: Calculate \( (1.04)^{2.5} \).
Using a calculator or logarithmic tables, we find:
\[ (1.04)^{2.5} \approx 1.1004 \]

### Step 5: Calculate the total amount (A).
Now, substituting back into the formula:
\[ A \approx 15625 \times 1.1004 \approx 17234.375 \]

### Step 6: Calculate the compound interest (CI).
The compound interest can be found by subtracting the principal from the total amount:
\[ CI = A - P \]
\[ CI \approx 17234.375 - 15625 \approx 1609.375 \]

### Final Answer:
The compound interest on Rs. 15625 for 2.5 years at 4% per annum is approximately Rs. 1609.38.

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