A sum of money was lent at 25% p.a.C.I. compounding annually. If the interest accrued for the second year only is Rs 3750, then find the sum.

Options

A. A)Rs.15000
B. B)Rs.12000
C. C)Rs.10000
D. D)Rs.16000

Answer

To solve the problem step by step, we will follow the principles of compound interest.

### Step 1: Understand the problem
We know that the interest accrued for the second year only is Rs 3750, and the rate of interest is 25% per annum.

### Step 2: Define the variables
Let the principal amount be \( P \). The rate of interest \( R \) is 25% per annum, which can be expressed as a fraction:
\[ R = \frac{25}{100} = \frac{1}{4} \]

### Step 3: Calculate the interest for the first and second year
In compound interest, the interest for the first year is calculated on the principal:
\[ \text{Interest for Year 1} = P \times R = P \times \frac{1}{4} = \frac{P}{4} \]

For the second year, the interest is calculated on the new principal, which is the original principal plus the interest from the first year:
\[ \text{New Principal for Year 2} = P + \frac{P}{4} = P \left(1 + \frac{1}{4}\right) = P \times \frac{5}{4} \]

Now, the interest for the second year will be:
\[ \text{Interest for Year 2} = \text{New Principal} \times R = P \times \frac{5}{4} \times \frac{1}{4} = \frac{5P}{16} \]

### Step 4: Set up the equation
According to the problem, the interest for the second year is Rs 3750:
\[ \frac{5P}{16} = 3750 \]

### Step 5: Solve for \( P \)
To find \( P \), multiply both sides by 16:
\[ 5P = 3750 \times 16 \]
\[ 5P = 60000 \]

Now, divide both sides by 5:
\[ P = \frac{60000}{5} = 12000 \]

### Conclusion
The principal amount \( P \) is Rs 12000.