Compound Interest on a sum of money is Rs. 350 in 4 years at `33(1)/(3)` % per annum. Find that sum.

Answer

To find the principal amount (sum of money) on which the compound interest is calculated, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Compound Interest (CI) = Rs. 350
- Time (t) = 4 years
- Rate of Interest (R) = \(33 \frac{1}{3}\% = \frac{100}{3}\%\)

2. **Convert the rate of interest into a decimal**:
- \(R = \frac{100}{3} \div 100 = \frac{1}{3}\)

3. **Use the formula for Compound Interest**:
The formula for Compound Interest is:
\[ CI = P \left( \left(1 + \frac{R}{100}\right)^t - 1 \right) \]
Where:
- \(P\) = Principal amount
- \(R\) = Rate of interest
- \(t\) = Time in years

4. **Substituting the known values into the formula**:
\[ 350 = P \left( \left(1 + \frac{1}{3}\right)^4 - 1 \right) \]

5. **Simplify the expression inside the parentheses**:
\[ 1 + \frac{1}{3} = \frac{4}{3} \]
Therefore,
\[ \left(\frac{4}{3}\right)^4 - 1 \]

6. **Calculate \(\left(\frac{4}{3}\right)^4\)**:
\[ \left(\frac{4}{3}\right)^4 = \frac{256}{81} \]

7. **Subtract 1 from \(\frac{256}{81}\)**:
\[ \frac{256}{81} - 1 = \frac{256}{81} - \frac{81}{81} = \frac{256 - 81}{81} = \frac{175}{81} \]

8. **Substituting back into the equation**:
\[ 350 = P \left(\frac{175}{81}\right) \]

9. **Solve for \(P\)**:
\[ P = 350 \times \frac{81}{175} \]

10. **Simplify the expression**:
- First, simplify \(350\) and \(175\):
\[ 350 \div 175 = 2 \]
- Therefore,
\[ P = 2 \times 81 = 162 \]

### Final Answer:
The principal amount is Rs. 162.

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