If the compound interest on a certain sum for 2 years at 3% p.a. is ₹ 101.50, then what will be the simple interest on the same sum at the same rate and for the same time

Answer

To find the simple interest on a certain sum given that the compound interest for 2 years at 3% per annum is ₹101.50, we can follow these steps:

### Step 1: Understand the given information
- Compound Interest (CI) for 2 years = ₹101.50
- Rate of interest (R) = 3% per annum
- Time (N) = 2 years

### Step 2: Use the formula for Compound Interest
The formula for the amount (A) after 2 years with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( N \) = Time in years

### Step 3: Calculate the amount using the compound interest
From the compound interest formula, we know:
\[ CI = A - P \]
Thus, we can express the compound interest as:
\[ 101.50 = P \left(1 + \frac{3}{100}\right)^2 - P \]

### Step 4: Simplify the equation
Now, substituting \( \left(1 + \frac{3}{100}\right)^2 \):
\[ 1 + \frac{3}{100} = 1.03 \]
So,
\[ (1.03)^2 = 1.0609 \]
Thus, the equation becomes:
\[ 101.50 = P \cdot 1.0609 - P \]
\[ 101.50 = P(1.0609 - 1) \]
\[ 101.50 = P \cdot 0.0609 \]

### Step 5: Solve for P (Principal)
Now, rearranging the equation to find \( P \):
\[ P = \frac{101.50}{0.0609} \]
Calculating this gives:
\[ P \approx 1665.75 \]

### Step 6: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \cdot R \cdot T}{100} \]
Substituting the values we have:
\[ SI = \frac{1665.75 \cdot 3 \cdot 2}{100} \]
Calculating this gives:
\[ SI = \frac{9994.5}{100} = 99.945 \approx 100 \]

### Step 7: Conclusion
Thus, the simple interest on the same sum at the same rate and for the same time is approximately ₹100.

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