The simple interest on a certain sum of money at the rate of 5% per annum for 8 years is Rs.840. Rate of interest for which the same amount of interest can be received on the same sum after 5 years is :

Options

A. 7 % per annum
B. 8 % per annum
C. 9 % annum
D. 10 % annum

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI):

**Formula for Simple Interest:**
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the initial sum of money)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Find the Principal Amount
Given:
- Simple Interest (SI) = Rs. 840
- Rate (R) = 5%
- Time (T) = 8 years

Using the formula:
\[ 840 = \frac{P \times 5 \times 8}{100} \]

### Step 2: Rearranging the equation
To find \( P \), rearrange the equation:
\[ P = \frac{840 \times 100}{5 \times 8} \]

### Step 3: Calculate the Principal Amount
Calculating the values:
\[ P = \frac{840 \times 100}{40} \]
\[ P = \frac{84000}{40} \]
\[ P = 2100 \]

So, the Principal Amount (P) is Rs. 2100.

### Step 4: Finding the new rate of interest
Now, we need to find the rate of interest (R) for which the same amount of interest (Rs. 840) can be received on the same sum (Rs. 2100) after 5 years.

Using the formula again:
\[ 840 = \frac{2100 \times R \times 5}{100} \]

### Step 5: Rearranging the equation for R
Rearranging to find \( R \):
\[ R = \frac{840 \times 100}{2100 \times 5} \]

### Step 6: Calculate the Rate of Interest
Calculating the values:
\[ R = \frac{84000}{10500} \]
\[ R = 8 \]

So, the rate of interest for which the same amount of interest can be received after 5 years is **8%**.

### Final Answer:
The rate of interest is **8%**.

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