Hans Kumar borrows 7000 at simple interest from the village moneylender. At the end of 3 years, he again borrows 3000 and closes his account after paying 4615 as interest after 8 years from the time he made the first borrowing. Find the rate of interest.

Options

A. `3.5%`
B. `4.5%`
C. `5.5%`
D. `6.5%`

Answer

To solve the problem step by step, we will break down the information given and use the formula for simple interest.

### Step 1: Understand the Borrowing Timeline
Hans Kumar borrows 7000 at the beginning. After 3 years, he borrows an additional 3000. The total time from the first borrowing to when he closes his account is 8 years.

### Step 2: Calculate the Time Period for Each Borrowing
- The first borrowing of 7000 is for 8 years.
- The second borrowing of 3000 is for 5 years (since he borrowed it after 3 years).

### Step 3: Use the Simple Interest Formula
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

### Step 4: Calculate Interest for Each Amount
1. **For the first borrowing of 7000 for 8 years:**
\[ \text{SI}_1 = \frac{7000 \times R \times 8}{100} = 560R \]

2. **For the second borrowing of 3000 for 5 years:**
\[ \text{SI}_2 = \frac{3000 \times R \times 5}{100} = 150R \]

### Step 5: Total Interest Paid
The total interest paid after 8 years is given as 4615. Therefore, we can set up the equation:
\[ 560R + 150R = 4615 \]

### Step 6: Combine Like Terms
Combine the terms on the left side:
\[ 710R = 4615 \]

### Step 7: Solve for R
To find the rate of interest \( R \), divide both sides by 710:
\[ R = \frac{4615}{710} \]

### Step 8: Calculate R
Now, perform the division:
\[ R = 6.5 \]

### Conclusion
The rate of interest is **6.5%**.

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