What sum of money will amount to Rs 5,445 in 2 years at 10% per annum compound interest?

Answer

To find the sum of money (principal) that will amount to Rs 5,445 in 2 years at a compound interest rate of 10% per annum, we can use the compound interest formula:

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

**Step 2: Identify the known values.**
From the question:
- \( A = 5445 \) (the amount after 2 years)
- \( R = 10\% \) (the rate of interest)
- \( n = 2 \) years (the time period)

**Step 3: Substitute the known values into the formula.**
We need to find \( P \):
\[ 5445 = P \left(1 + \frac{10}{100}\right)^2 \]

**Step 4: Simplify the equation.**
Calculate \( 1 + \frac{10}{100} \):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
Now substitute this back into the equation:
\[ 5445 = P \left(1.1\right)^2 \]

**Step 5: Calculate \( (1.1)^2 \).**
\[ (1.1)^2 = 1.1 \times 1.1 = 1.21 \]
So the equation becomes:
\[ 5445 = P \times 1.21 \]

**Step 6: Solve for \( P \).**
To find \( P \), divide both sides by 1.21:
\[ P = \frac{5445}{1.21} \]

**Step 7: Perform the division.**
Calculating \( \frac{5445}{1.21} \):
\[ P = 4500 \]

Thus, the principal amount \( P \) is Rs 4,500.

### Final Answer:
The sum of money that will amount to Rs 5,445 in 2 years at 10% per annum compound interest is Rs 4,500.