If interest being compounded annually what sum will amount to `Rs. 2508.8` in 2 years at the rate of `12%` per annum at compound Interest?

Options

A. `Rs. 2000`
B. `Rs. 2200`
C. `Rs. 1800 `
D. `Rs. 2500 `

Answer

To find the principal sum (P) that will amount to Rs. 2508.8 in 2 years at a compound interest rate of 12% per annum, we can use the formula for compound interest:

\[ A = P(1 + r)^n \]

Where:
- \( A \) is the amount after time \( n \) (which is Rs. 2508.8),
- \( P \) is the principal amount (the sum we want to find),
- \( r \) is the rate of interest (12% or 0.12),
- \( n \) is the number of years (2 years).

### Step 1: Substitute the known values into the formula

We know:
- \( A = 2508.8 \)
- \( r = 12\% = 0.12 \)
- \( n = 2 \)

Substituting these values into the formula gives:

\[ 2508.8 = P(1 + 0.12)^2 \]

### Step 2: Calculate \( (1 + r)^n \)

Now, calculate \( (1 + 0.12)^2 \):

\[ (1 + 0.12) = 1.12 \]

Now square it:

\[ (1.12)^2 = 1.2544 \]

### Step 3: Substitute back into the equation

Now substitute \( (1.12)^2 \) back into the equation:

\[ 2508.8 = P \times 1.2544 \]

### Step 4: Solve for \( P \)

To find \( P \), divide both sides by \( 1.2544 \):

\[ P = \frac{2508.8}{1.2544} \]

### Step 5: Calculate \( P \)

Now perform the division:

\[ P \approx 2000 \]

Thus, the principal amount (sum) that will amount to Rs. 2508.8 in 2 years at a compound interest rate of 12% per annum is approximately Rs. 2000.

### Final Answer:
The sum is Rs. 2000.

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