In how much time will a sum of money triple itself at `25%` per annum ?

Answer

To solve the problem of how much time it will take for a sum of money to triple itself at an interest rate of 25% per annum, we can follow these steps:

### Step 1: Understand the Problem
We need to find the time (t) it takes for a principal amount (P) to triple. If we denote the principal as \( P \), then the amount after time \( t \) will be \( 3P \).

### Step 2: Set Up the Formula
The formula for calculating the amount (A) using simple interest is:
\[ A = P + I \]
Where \( I \) (Interest) can be calculated using the formula:
\[ I = \frac{P \cdot r \cdot t}{100} \]
Here, \( r \) is the rate of interest.

### Step 3: Substitute the Values
In this case:
- The amount \( A = 3P \)
- The principal \( P = P \)
- The rate \( r = 25\% \)

Substituting these into the formula gives:
\[ 3P = P + \frac{P \cdot 25 \cdot t}{100} \]

### Step 4: Simplify the Equation
Now, we can simplify the equation:
\[ 3P = P + \frac{25Pt}{100} \]
Subtract \( P \) from both sides:
\[ 3P - P = \frac{25Pt}{100} \]
This simplifies to:
\[ 2P = \frac{25Pt}{100} \]

### Step 5: Cancel Out the Principal
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ 2 = \frac{25t}{100} \]

### Step 6: Solve for Time
Now, we can solve for \( t \):
\[ 2 = \frac{25t}{100} \]
Multiply both sides by 100:
\[ 200 = 25t \]
Now, divide both sides by 25:
\[ t = \frac{200}{25} = 8 \]

### Conclusion
The time required for the sum of money to triple itself at a rate of 25% per annum is **8 years**.

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