What is the rate (in per cent) of simple interest at which a sum of money become three times of itself in 50 years ?

Options

A. 2
B. 4
C. 5
D. 8

Answer

To find the rate of simple interest at which a sum of money becomes three times itself in 50 years, we can follow these steps:

### Step 1: Understand the relationship between Principal, Amount, and Simple Interest
The formula for the amount (A) in terms of Principal (P), Rate (R), and Time (T) in simple interest is:
\[ A = P + SI \]
Where \( SI \) is the Simple Interest.

### Step 2: Define the terms
Let the Principal amount be \( P \). According to the question, the amount becomes three times the principal in 50 years. Therefore:
\[ A = 3P \]

### Step 3: Calculate the Simple Interest
The Simple Interest (SI) can be calculated as:
\[ SI = A - P \]
Substituting the value of A:
\[ SI = 3P - P = 2P \]

### Step 4: Use the Simple Interest formula
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) is the Simple Interest
- \( P \) is the Principal
- \( R \) is the Rate of interest
- \( T \) is the Time in years

### Step 5: Substitute the known values
From the previous steps, we know:
- \( SI = 2P \)
- \( T = 50 \)

Substituting these into the SI formula gives:
\[ 2P = \frac{P \times R \times 50}{100} \]

### Step 6: Simplify the equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = \frac{R \times 50}{100} \]

### Step 7: Solve for R
To isolate R, multiply both sides by 100:
\[ 200 = R \times 50 \]
Now divide both sides by 50:
\[ R = \frac{200}{50} = 4 \]

### Step 8: Conclusion
Thus, the rate of simple interest is:
\[ R = 4\% \]