A certain sum amounts to Rs 72900 in 2 years at 8% per annum compound interest, compounded annually. Find the sum.

Answer

To find the principal amount (P) that amounts to Rs 72,900 in 2 years at an 8% per annum compound interest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Amount (A) = Rs 72,900
- Rate of interest (r) = 8% per annum
- Time (n) = 2 years

2. **Use the Compound Interest Formula:**
The formula for the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Substituting the known values into the formula:
\[ 72,900 = P \left(1 + \frac{8}{100}\right)^2 \]

3. **Calculate the Value Inside the Parentheses:**
\[ 1 + \frac{8}{100} = 1 + 0.08 = 1.08 \]
Now substitute this back into the equation:
\[ 72,900 = P \times (1.08)^2 \]

4. **Calculate \((1.08)^2\):**
\[ (1.08)^2 = 1.1664 \]
Now the equation becomes:
\[ 72,900 = P \times 1.1664 \]

5. **Solve for P:**
To find P, divide both sides by 1.1664:
\[ P = \frac{72,900}{1.1664} \]

6. **Perform the Division:**
\[ P = 62,500 \]

### Final Answer:
The principal amount (P) is Rs 62,500.

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