On what sum of money will compound intersect for 2 year at 5 percent per year amount to Rs 64 ?

Answer

To solve the problem of finding the principal sum of money on which compound interest for 2 years at a rate of 5% per year amounts to Rs 64, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Compound Interest (CI) = Rs 64
- Rate of Interest (R) = 5% per annum
- Time (T) = 2 years

2. **Understand the Formula for Compound Interest:**
The formula for the amount (A) after time T with principal (P) is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
where:
- A = Total amount after T years
- P = Principal amount
- R = Rate of interest
- T = Time in years

3. **Express the Total Amount (A):**
Since the compound interest (CI) is given, we can express the total amount as:
\[ A = P + CI \]
Therefore:
\[ A = P + 64 \]

4. **Substitute the Amount in the Formula:**
Now substitute A in the compound interest formula:
\[ P + 64 = P \left(1 + \frac{5}{100}\right)^2 \]

5. **Calculate the Growth Factor:**
Calculate \(1 + \frac{5}{100}\):
\[ 1 + \frac{5}{100} = 1.05 \]
Now square it for 2 years:
\[ (1.05)^2 = 1.1025 \]

6. **Set Up the Equation:**
Substitute this back into the equation:
\[ P + 64 = P \times 1.1025 \]

7. **Rearrange the Equation:**
Rearranging gives:
\[ P \times 1.1025 - P = 64 \]
\[ P(1.1025 - 1) = 64 \]
\[ P(0.1025) = 64 \]

8. **Solve for P:**
Now, divide both sides by 0.1025:
\[ P = \frac{64}{0.1025} \]
\[ P = 624.39 \]

### Final Answer:
The sum of money (Principal) is approximately Rs 624.39.