A sum of money put at simple interest trebles itself in 15 years. The rate per cent per annum is

Options

A. `13 1/3`
B. `16 2/3`
C. `12 2/3`
D. `20%`

Answer

To find the rate of simple interest at which a sum of money triples itself in 15 years, we can follow these steps:

### Step 1: Understand the Problem
We know that a sum of money triples itself in 15 years. This means if we start with a principal amount \( P \), after 15 years, the amount \( A \) will be \( 3P \).

### Step 2: Calculate the Simple Interest
The simple interest (SI) can be calculated using the formula:
\[ SI = A - P \]
Substituting the values we have:
\[ SI = 3P - P = 2P \]

### Step 3: Use the Simple Interest Formula
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 4: Substitute Known Values
From the previous steps, we know:
- \( SI = 2P \)
- \( T = 15 \) years

Substituting these into the simple interest formula gives:
\[ 2P = \frac{P \times R \times 15}{100} \]

### Step 5: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 2 = \frac{R \times 15}{100} \]

### Step 6: Solve for \( R \)
To isolate \( R \), we multiply both sides by 100:
\[ 200 = R \times 15 \]
Now, divide both sides by 15:
\[ R = \frac{200}{15} \]

### Step 7: Simplify the Rate
Calculating \( \frac{200}{15} \):
\[ R = \frac{40}{3} \approx 13.33\% \]
This can also be expressed as \( 13 \frac{1}{3}\% \).

### Conclusion
Thus, the rate of interest per annum is \( 13 \frac{1}{3}\% \).

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