A person made a fixed deposit of Rs. 30,000 ina bank for 5 years at 10 % simple interest per annum. He had to withdraw the whole amount after 3 years to meet the expenses of his daughter's marriage and he received Rs. 7800 less than what he would have got after 5 years. What is the rate of simple interest per annum paid by the bank for this premature encashment ?

Options

A. 0.06
B. 0.07
C. 0.08
D. 0.09

Answer

To solve the problem step-by-step, we will follow the information given in the question and apply the formula for simple interest.

### Step 1: Calculate the total amount after 5 years
The formula for calculating the total amount (A) after a certain time with simple interest is:
\[ A = P + SI \]
Where:
- \( P \) = Principal amount
- \( SI \) = Simple Interest

The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]

Given:
- Principal \( P = 30,000 \)
- Rate \( R = 10\% \)
- Time \( T = 5 \) years

First, we calculate the Simple Interest for 5 years:
\[ SI = \frac{30,000 \times 10 \times 5}{100} \]
\[ SI = \frac{30,000 \times 50}{100} \]
\[ SI = 15,000 \]

Now, calculate the total amount after 5 years:
\[ A = 30,000 + 15,000 = 45,000 \]

### Step 2: Calculate the amount received after 3 years
Now, we need to find out how much he would receive after 3 years.

Using the same formula for Simple Interest:
- Time \( T = 3 \) years

Calculate the Simple Interest for 3 years:
\[ SI = \frac{30,000 \times 10 \times 3}{100} \]
\[ SI = \frac{30,000 \times 30}{100} \]
\[ SI = 9,000 \]

Now, calculate the total amount after 3 years:
\[ A = 30,000 + 9,000 = 39,000 \]

### Step 3: Determine the difference in amounts
According to the question, the amount received after 3 years is Rs. 7,800 less than what he would have received after 5 years.

So, we set up the equation:
\[ 39,000 = 45,000 - 7,800 \]

### Step 4: Calculate the premature encashment interest rate
Let the rate of interest for the premature encashment be \( R' \).

The amount he would have received if he had kept the money for 3 years at the new rate \( R' \) is:
\[ A' = P + SI' \]
Where:
\[ SI' = \frac{30,000 \times R' \times 3}{100} \]

From the information given, we know:
\[ A' = 39,000 \]

So, we can write:
\[ 39,000 = 30,000 + \frac{30,000 \times R' \times 3}{100} \]

Rearranging gives:
\[ 39,000 - 30,000 = \frac{30,000 \times R' \times 3}{100} \]
\[ 9,000 = \frac{30,000 \times R' \times 3}{100} \]

### Step 5: Solve for \( R' \)
Multiply both sides by 100:
\[ 9,000 \times 100 = 30,000 \times R' \times 3 \]
\[ 900,000 = 90,000 \times R' \]

Now, divide both sides by 90,000:
\[ R' = \frac{900,000}{90,000} \]
\[ R' = 10 \]

### Final Step: Conclusion
The rate of simple interest per annum paid by the bank for this premature encashment is:
\[ R' = 10\% \]