The compound interest on a certain sum invested for 2 years at 10% per annum is Rs 1,522.50, the interest being compounded yearly. The sum is:

Options

A. Rs 7,250
B. Rs 7,200
C. Rs 7,500
D. Rs 7,000

Answer

To find the principal sum (P) that results in a compound interest of Rs 1,522.50 over 2 years at an interest rate of 10% per annum, we can use the formula for compound interest.

### Step-by-Step Solution:

1. **Understand the Compound Interest Formula**:
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where:
- \( A \) = the total amount after time \( n \)
- \( P \) = the principal amount (the initial sum)
- \( r \) = the rate of interest per annum
- \( n \) = the number of years the money is invested or borrowed

2. **Identify Given Values**:
- Compound Interest (CI) = Rs 1,522.50
- Rate (r) = 10%
- Time (n) = 2 years

3. **Calculate Total Amount (A)**:
Since the compound interest is the total amount minus the principal, we can express this as:
\[ CI = A - P \]
Thus, we can rewrite it as:
\[ A = P + CI \]
Substituting the given CI:
\[ A = P + 1,522.50 \]

4. **Substitute into the Compound Interest Formula**:
Now we can substitute \( A \) into the compound interest formula:
\[ P + 1,522.50 = P \left(1 + \frac{10}{100}\right)^2 \]
Simplifying the right side:
\[ P + 1,522.50 = P \left(1 + 0.1\right)^2 = P \left(1.1\right)^2 = P \cdot 1.21 \]

5. **Rearranging the Equation**:
Now we can rearrange the equation:
\[ P + 1,522.50 = 1.21P \]
Subtract \( P \) from both sides:
\[ 1,522.50 = 1.21P - P \]
\[ 1,522.50 = 0.21P \]

6. **Solve for P**:
Now, divide both sides by 0.21 to find \( P \):
\[ P = \frac{1,522.50}{0.21} \]
\[ P = 7,250 \]

### Final Answer:
The sum (principal amount) is Rs 7,250.