At what rate per cent will a sum of money triple itself in `12` years ?

Answer

To find the rate at which a sum of money will triple itself in 12 years, we can follow these steps:

### Step 1: Define the Variables
Let the principal amount be \( P \).
The time period \( T \) is given as 12 years.
The amount \( A \) after 12 years will be \( 3P \) (since the amount triples).

### Step 2: Calculate the Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = A - P \]
Substituting the values we have:
\[ SI = 3P - P = 2P \]

### Step 3: Use the Simple Interest Formula
The formula for Simple Interest is also given by:
\[ SI = \frac{P \times R \times T}{100} \]
Where \( R \) is the rate of interest. We can set the two expressions for SI equal to each other:
\[ 2P = \frac{P \times R \times 12}{100} \]

### Step 4: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = \frac{R \times 12}{100} \]

### Step 5: Solve for \( R \)
Now, we can multiply both sides by 100 to eliminate the fraction:
\[ 200 = R \times 12 \]
Next, divide both sides by 12 to isolate \( R \):
\[ R = \frac{200}{12} \]

### Step 6: Simplify \( R \)
Now, simplify \( \frac{200}{12} \):
\[ R = \frac{200 \div 4}{12 \div 4} = \frac{50}{3} \]

### Step 7: Convert to Mixed Number
To convert \( \frac{50}{3} \) into a mixed number:
\[ 50 \div 3 = 16 \quad \text{(remainder 2)} \]
Thus, we can express it as:
\[ R = 16 \frac{2}{3} \]

### Final Answer
The rate at which a sum of money will triple itself in 12 years is \( 16 \frac{2}{3} \% \).

---