If Rs. 12,500 is invested at `12%` p.a. on compound interest for one year and 4 months. compounded annually. then the amount received is

Options

A. Rs. 14,650
B. Rs. 14,560
C. Rs. 15,460
D. Rs. 15,460

Answer

To solve the problem of calculating the amount received after investing Rs. 12,500 at a compound interest rate of 12% per annum for 1 year and 4 months, we can follow these steps:

### Step 1: Convert the time period into years
The total time period is given as 1 year and 4 months. We need to express this in years.

1 year = 12 months
4 months = 4/12 years = 1/3 years

So, the total time period in years is:
\[ 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \text{ years} \]

### Step 2: Identify the principal and rate of interest
- Principal (P) = Rs. 12,500
- Rate of interest (R) = 12% per annum

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where:
- \( A \) = Amount after time \( T \)
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

Substituting the values we have:
\[ A = 12500 \left(1 + \frac{12}{100}\right)^{\frac{4}{3}} \]

### Step 4: Simplify the expression
Calculate \( 1 + \frac{12}{100} \):
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

Now substitute this back into the formula:
\[ A = 12500 \times (1.12)^{\frac{4}{3}} \]

### Step 5: Calculate \( (1.12)^{\frac{4}{3}} \)
To calculate \( (1.12)^{\frac{4}{3}} \), we can first find \( (1.12)^4 \) and then take the cube root.

Calculating \( (1.12)^4 \):
\[ (1.12)^4 \approx 1.5748 \]

Now, take the cube root:
\[ (1.5748)^{\frac{1}{3}} \approx 1.1447 \]

### Step 6: Calculate the final amount
Now substitute back into the amount formula:
\[ A \approx 12500 \times 1.1447 \approx 14308.75 \]

### Final Answer
The amount received after 1 year and 4 months is approximately Rs. 14,308.75.

---