At what rate of simple interest per annum will a sum triple itself in 8 years ?
A)`12.5%`
B)`33.3%`
C)`10%`
D)`25%`

Options

A. `12.5%`
B. `33.3%`
C. `10%`
D. `25%`

Answer

To find the rate of simple interest per annum at which a sum triples itself in 8 years, we can follow these steps:

### Step 1: Understand the Problem
We need to determine the rate of simple interest that allows a principal amount to triple in 8 years. If the principal amount is P, after 8 years it becomes 3P.

### Step 2: Calculate the Total Interest Earned
If the principal amount triples, the total amount after 8 years is:
\[ \text{Total Amount} = 3P \]
The interest earned (I) over 8 years is:
\[ I = \text{Total Amount} - \text{Principal} = 3P - P = 2P \]

### Step 3: Use the Simple Interest Formula
The formula for simple interest is given by:
\[ I = P \times r \times t \]
Where:
- \( I \) is the interest earned,
- \( P \) is the principal amount,
- \( r \) is the rate of interest per annum (in decimal),
- \( t \) is the time in years.

### Step 4: Substitute Known Values
From our previous calculation, we know:
- \( I = 2P \)
- \( t = 8 \) years

Substituting these values into the simple interest formula:
\[ 2P = P \times r \times 8 \]

### Step 5: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = r \times 8 \]

### Step 6: Solve for \( r \)
Now, divide both sides by 8 to find \( r \):
\[ r = \frac{2}{8} = \frac{1}{4} \]

### Step 7: Convert to Percentage
To express \( r \) as a percentage, multiply by 100:
\[ r = \frac{1}{4} \times 100 = 25\% \]

### Conclusion
The rate of simple interest per annum at which a sum triples itself in 8 years is **25%**. Therefore, the correct answer is option D) 25%.

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