The compound interest on a certain sum of money invested for 2 years at 5% per annum is Rs. 328. The simple interest on the sum, at the same rate and for the same period will be

Answer

To solve the problem step by step, we will first find the principal amount using the given compound interest and then calculate the simple interest.

### Step 1: Understanding the given information
We know:
- Compound Interest (CI) = Rs. 328
- Rate (R) = 5% per annum
- Time (T) = 2 years

### Step 2: 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

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 328 = P \left( \left(1 + \frac{5}{100}\right)^2 - 1 \right) \]

### Step 4: Simplify the expression
Calculate \( \left(1 + \frac{5}{100}\right)^2 \):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]
Now, calculate \( 1.05^2 \):
\[ 1.05^2 = 1.1025 \]
Now substitute this back into the equation:
\[ 328 = P \left( 1.1025 - 1 \right) \]
\[ 328 = P \times 0.1025 \]

### Step 5: Solve for Principal (P)
Now, isolate \( P \):
\[ P = \frac{328}{0.1025} \]
Calculating this gives:
\[ P = 3200 \]

### Step 6: Calculate Simple Interest (SI)
Now that we have the principal, we can calculate the Simple Interest using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{3200 \times 5 \times 2}{100} \]

### Step 7: Simplify the Simple Interest calculation
Calculating this gives:
\[ SI = \frac{32000}{100} = 320 \]

### Final Answer
The Simple Interest on the sum, at the same rate and for the same period, will be Rs. 320.

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