A certain sum of money becomes 3 times of itself in 50years. Find the Rate of interest.

Answer

To solve the problem step by step, we will follow the principles of simple interest.

### Step 1: Define the Variables
Let:
- \( P \) = Principal amount (the initial sum of money)
- \( A \) = Amount after 50 years
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Determine the Amount
According to the problem, the amount becomes 3 times the principal after 50 years. Therefore:
\[ A = 3P \]

### Step 3: Write the Formula for Simple Interest
The formula for the amount in simple interest is:
\[ A = P + \text{SI} \]
Where SI (Simple Interest) is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

### Step 4: Substitute the Known Values
Substituting the values we have:
\[ 3P = P + \frac{P \times R \times 50}{100} \]

### Step 5: Simplify the Equation
Now, we can simplify this equation:
1. Subtract \( P \) from both sides:
\[ 3P - P = \frac{P \times R \times 50}{100} \]
\[ 2P = \frac{P \times R \times 50}{100} \]

2. Cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = \frac{R \times 50}{100} \]

### Step 6: Solve for R
To isolate \( R \), multiply both sides by 100:
\[ 200 = R \times 50 \]

Now, divide both sides by 50:
\[ R = \frac{200}{50} \]
\[ R = 4 \]

### Conclusion
The rate of interest is:
\[ R = 4\% \text{ per annum} \]

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