Amit takes some loan from Akash for 2 yr at the rate of 5% per annum and after 2 yr he gave back ? 6600 to Akash and completed the payment of his loan. Find the interest paid by Amit.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Identify the given information
- **Loan Duration (Time)**: 2 years
- **Rate of Interest**: 5% per annum
- **Total Amount Paid Back**: ₹6600

### Step 2: Understand the relationship between Principal, Interest, and Amount
The formula for the total amount (A) paid back after a certain period is:
\[ A = P + I \]
Where:
- \( A \) = Total Amount paid back
- \( P \) = Principal (the original loan amount)
- \( I \) = Simple Interest

### Step 3: Write the formula for Simple Interest
The formula for Simple Interest (I) is:
\[ I = \frac{P \times R \times T}{100} \]
Where:
- \( R \) = Rate of interest (5%)
- \( T \) = Time (2 years)

### Step 4: Substitute the known values into the formula for Amount
From the relationship established in Step 2, we can express the total amount paid back as:
\[ 6600 = P + I \]
Substituting the formula for Simple Interest into this equation gives:
\[ 6600 = P + \frac{P \times 5 \times 2}{100} \]

### Step 5: Simplify the equation
This can be simplified to:
\[ 6600 = P + \frac{10P}{100} \]
\[ 6600 = P + 0.1P \]
\[ 6600 = 1.1P \]

### Step 6: Solve for Principal (P)
To find the principal \( P \), rearrange the equation:
\[ P = \frac{6600}{1.1} \]
Calculating this gives:
\[ P = 6000 \]

### Step 7: Calculate the Simple Interest (I)
Now that we have the principal, we can calculate the Simple Interest:
\[ I = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ I = \frac{6000 \times 5 \times 2}{100} \]
\[ I = \frac{60000}{100} \]
\[ I = 600 \]

### Conclusion
The interest paid by Amit is ₹600.

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