A certain sum will amount of ₹12,100 in 2 years at 10% per annum off compound interest. interest being compounded annually. The sum is:

Options

A. ₹1,200
B. ₹6,000
C. ₹8,000
D. ₹10,000

Explanation

To find the principal amount that will amount to ₹12,100 in 2 years at a compound interest rate of 10% per annum, we can use the formula for compound interest:

**Step 1: Write down the formula for compound interest.**
The formula for the amount \( A \) after \( n \) years is given by:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
where:
- \( A \) = Amount after \( n \) years
- \( P \) = Principal amount (the initial sum)
- \( r \) = Rate of interest per annum
- \( n \) = Time in years

**Step 2: Substitute the known values into the formula.**
Given:
- \( A = 12,100 \)
- \( r = 10\% \)
- \( n = 2 \)

Substituting these values into the formula:
\[ 12,100 = P \left(1 + \frac{10}{100}\right)^2 \]

**Step 3: Simplify the equation.**
Calculating \( 1 + \frac{10}{100} \):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
Now, substituting this back into the equation:
\[ 12,100 = P \times (1.1)^2 \]
Calculating \( (1.1)^2 \):
\[ (1.1)^2 = 1.21 \]
Thus, the equation becomes:
\[ 12,100 = P \times 1.21 \]

**Step 4: Solve for \( P \).**
To find \( P \), divide both sides by 1.21:
\[ P = \frac{12,100}{1.21} \]

**Step 5: Perform the division.**
Calculating \( \frac{12,100}{1.21} \):
\[ P = 10,000 \]

Thus, the principal amount is ₹10,000.

### Summary of the Solution:
The sum (principal amount) that will amount to ₹12,100 in 2 years at a compound interest rate of 10% per annum is ₹10,000.