An amount becomes twice in 15 years at simple interest. Find the rate%

Options

A. 20/3 %
B. 17/5 %
C. 16/3 %
D. 22/7 %

Answer

To solve the problem of finding the rate of simple interest at which an amount doubles in 15 years, we can follow these steps:

### Step 1: Understand the Problem
We know that the amount doubles in 15 years under simple interest. If we denote the principal amount as \( P \), then the amount after 15 years will be \( 2P \).

### Step 2: Use the Simple Interest Formula
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest (in %)
- \( T \) = Time (in years)

### Step 3: Relate the Amount to Principal and Simple Interest
The total amount \( A \) after time \( T \) can be expressed as:
\[ A = P + SI \]
Since the amount doubles, we have:
\[ 2P = P + SI \]
From this, we can deduce that:
\[ SI = 2P - P = P \]

### Step 4: Substitute SI in the Formula
Now we substitute \( SI \) back into the simple interest formula:
\[ P = \frac{P \times R \times 15}{100} \]

### Step 5: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1 = \frac{R \times 15}{100} \]

### Step 6: Solve for R
To find \( R \), we rearrange the equation:
\[ R \times 15 = 100 \]
\[ R = \frac{100}{15} = \frac{20}{3} \]

### Step 7: Convert to Percentage
Thus, the rate of interest is:
\[ R = \frac{20}{3} \text{ percent} \]

### Final Answer
The rate of interest is \( \frac{20}{3} \% \).

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