If a sum of money diposited in a bank at simple interest is double in 6 year then after 12 year the amount will be ?

Options

A. 3
B. 4
C. 2
D. 1

Answer

To solve the problem step by step, we need to understand the concept of simple interest and how it relates to the principal amount, rate of interest, and time.

### Step 1: Understand the Given Information
We know that a sum of money deposited in a bank at simple interest doubles in 6 years. This means that the total amount after 6 years is twice the principal amount.

Let the principal amount be \( P \). Therefore, after 6 years, the amount \( A \) will be:
\[ A = 2P \]

### Step 2: Calculate the Simple Interest
The formula for simple interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

Since the amount after 6 years is \( 2P \), we can express this as:
\[ A = P + SI \]
Substituting the expression for \( SI \):
\[ 2P = P + \frac{P \times R \times 6}{100} \]

### Step 3: Simplify the Equation
Rearranging the equation gives:
\[ 2P - P = \frac{P \times R \times 6}{100} \]
\[ P = \frac{P \times R \times 6}{100} \]

### Step 4: Cancel \( P \) from Both Sides
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ 1 = \frac{R \times 6}{100} \]

### Step 5: Solve for Rate of Interest \( R \)
Multiplying both sides by 100 gives:
\[ 100 = R \times 6 \]
Now, divide by 6:
\[ R = \frac{100}{6} \]
\[ R = \frac{50}{3} \approx 16.67\% \]

### Step 6: Calculate the Amount After 12 Years
Now, we need to find the amount after 12 years. Using the simple interest formula again:
\[ SI = \frac{P \times R \times T}{100} \]
For \( T = 12 \) years:
\[ SI = \frac{P \times \frac{50}{3} \times 12}{100} \]
\[ SI = \frac{P \times 50 \times 12}{300} \]
\[ SI = \frac{600P}{300} \]
\[ SI = 2P \]

### Step 7: Find the Total Amount After 12 Years
Now, the total amount \( A \) after 12 years will be:
\[ A = P + SI \]
\[ A = P + 2P \]
\[ A = 3P \]

### Conclusion
Thus, after 12 years, the amount will be \( 3P \).

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