At what rate per cent per annum will be a sum of money treble in 25 years?

Options

A. a) 2 %
B. b) 4 %
C. c) 8 %
D. d) 16 %

Answer

To find the rate per cent per annum at which a sum of money will treble in 25 years, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( P \) = Principal amount (initial sum of money)
- \( A \) = Amount after 25 years
- \( R \) = Rate of interest per annum
- \( T \) = Time in years (which is 25 years)

### Step 2: Understand the Relationship
According to the problem, the amount after 25 years is three times the principal. Therefore, we can express this as:
\[ A = 3P \]

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

### Step 4: Use the Simple Interest Formula
The formula for Simple Interest is also given by:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values we have:
\[ 2P = \frac{P \times R \times 25}{100} \]

### Step 5: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = \frac{R \times 25}{100} \]

### Step 6: Solve for \( R \)
To isolate \( R \), we can multiply both sides by 100:
\[ 200 = R \times 25 \]
Now, divide both sides by 25:
\[ R = \frac{200}{25} = 8 \]

### Conclusion
The rate of interest \( R \) is 8% per annum.

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