A certain sum of money becomes 35 times of itself in 17 years . Find the Rate of Interest.

Answer

To find the rate of interest when a certain sum of money becomes 35 times itself in 17 years, we can follow these steps:

### Step 1: Define the Variables
Let the principal amount be \( P \). According to the problem, the amount after 17 years becomes \( 35P \).

### Step 2: Write the Formula for Amount
In the case of simple interest, the formula for the amount \( A \) is given by:
\[ A = P + \text{Simple Interest} \]
Where Simple Interest (SI) is calculated as:
\[ SI = \frac{P \times R \times T}{100} \]
Here, \( R \) is the rate of interest, and \( T \) is the time in years.

### Step 3: Substitute the Known Values
From the problem, we know:
\[ A = 35P \quad \text{and} \quad T = 17 \text{ years} \]
So we can write:
\[ 35P = P + \frac{P \times R \times 17}{100} \]

### Step 4: Simplify the Equation
Rearranging the equation gives:
\[ 35P - P = \frac{P \times R \times 17}{100} \]
This simplifies to:
\[ 34P = \frac{P \times R \times 17}{100} \]

### Step 5: Cancel Out \( P \)
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ 34 = \frac{R \times 17}{100} \]

### Step 6: Solve for \( R \)
Now, multiply both sides by 100 to eliminate the fraction:
\[ 3400 = R \times 17 \]
Next, divide both sides by 17 to isolate \( R \):
\[ R = \frac{3400}{17} \]

### Step 7: Calculate \( R \)
Calculating the right-hand side gives:
\[ R = 200 \]

### Conclusion
Thus, the rate of interest is:
\[ \text{Rate of Interest} = 200\% \text{ per annum} \]

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