A man borrows Rs. 6000 from a bank at simple interest. After 4 years, he paid Rs. 2500 to the bank and at the end of 5 years from the date of borrowing he paid Rs. 4560 to settle the account. Find the rate percent per annum.

Options

A. 4
B. 3
C. 3.85
D. 4.5

Answer

To solve the problem step by step, we will follow the outlined approach and calculations:

### Step 1: Understand the Problem
A man borrows Rs. 6000 at simple interest. He makes two payments: Rs. 2500 after 4 years and Rs. 4560 at the end of 5 years. We need to find the rate of interest per annum.

### Step 2: Calculate the Total Payment Made
The total amount paid by the man to the bank after 5 years is:
\[ \text{Total Payment} = 2500 + 4560 = 7060 \]

### Step 3: Calculate the Total Interest Paid
The total interest paid can be calculated by subtracting the principal from the total payment:
\[ \text{Total Interest} = \text{Total Payment} - \text{Principal} \]
\[ \text{Total Interest} = 7060 - 6000 = 1060 \]

### Step 4: Calculate the Interest for the First 4 Years
The interest for the first 4 years can be calculated using the formula for simple interest:
\[ \text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time} / 100 \]
Let \( R \) be the rate of interest. The interest for the first 4 years is:
\[ \text{Interest for 4 years} = 6000 \times R \times 4 / 100 \]

### Step 5: Calculate the Remaining Principal After 4 Years
After 4 years, the man pays Rs. 2500. The remaining principal after this payment is:
\[ \text{Remaining Principal} = 6000 + \text{Interest for 4 years} - 2500 \]

### Step 6: Calculate the Interest for the 5th Year
The interest for the 5th year on the remaining principal can be calculated:
\[ \text{Interest for 5th year} = \text{Remaining Principal} \times R \times 1 / 100 \]

### Step 7: Set Up the Equation
The total interest paid over the 5 years is the sum of the interest for the first 4 years and the interest for the 5th year:
\[ 1060 = \left(6000 \times R \times 4 / 100\right) + \left(\text{Remaining Principal} \times R \times 1 / 100\right) \]

### Step 8: Substitute and Solve for R
Substituting the remaining principal into the equation:
\[ 1060 = \left(6000 \times R \times 4 / 100\right) + \left((6000 + (6000 \times R \times 4 / 100) - 2500) \times R \times 1 / 100\right) \]
This simplifies to:
\[ 1060 = 240R + (3500 + 240R)R / 100 \]

### Step 9: Combine Like Terms
Combine the terms and solve for \( R \):
\[ 1060 = 240R + 35R \]
\[ 1060 = 275R \]

### Step 10: Solve for R
Now, isolate \( R \):
\[ R = \frac{1060}{275} \approx 3.85 \]

### Final Answer
The rate of interest per annum is approximately **3.85%**.

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