A sum at simple interest of 4% per annum amounts to ? 3120 in 5 yr. Find the sum

Answer

To solve the problem step by step, we will use the formula for simple interest and the relationship between principal, interest, and amount.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Rate of interest (R) = 4% per annum
- Time (T) = 5 years
- Amount (A) = ₹3120

2. **Recall the Formula for Simple Interest:**
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where P is the principal amount.

3. **Relate Amount to Principal and Simple Interest:**
The amount (A) is given by the formula:
\[ A = P + SI \]
Substituting the formula for SI, we get:
\[ A = P + \frac{P \times R \times T}{100} \]

4. **Substituting the Known Values:**
Substitute A = ₹3120, R = 4%, and T = 5 into the equation:
\[ 3120 = P + \frac{P \times 4 \times 5}{100} \]

5. **Simplifying the Equation:**
Calculate the simple interest term:
\[ \frac{4 \times 5}{100} = \frac{20}{100} = 0.2 \]
Thus, the equation becomes:
\[ 3120 = P + 0.2P \]
This simplifies to:
\[ 3120 = 1.2P \]

6. **Solving for P:**
To find P, divide both sides by 1.2:
\[ P = \frac{3120}{1.2} \]
Performing the division:
\[ P = 2600 \]

7. **Conclusion:**
The principal amount (sum) is ₹2600.

### Summary of the Solution:
The sum (principal amount) is ₹2600.

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