In how many years will an amount be doubled at 28.75% annual rate of interest?
(a)3.9
(b)3.47
(c)6.00
(d)3.00

Options

A. 3.9
B. 3.47
C. `6.00`
D. `3.00`

Answer

To determine how many years it will take for an amount to double at an annual interest rate of 28.75%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We want to find the time (T) it takes for an initial amount (Principal, P) to double at a given interest rate (R). If we start with P = 1, then the final amount (A) will be 2.

2. **Identify the Simple Interest Formula**: The formula for simple interest is:
\[ \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \]
where:
- P = Principal amount
- R = Rate of interest per annum
- T = Time in years

3. **Calculate the Simple Interest Needed**: Since we want to double the amount, the simple interest (SI) required is:
\[ SI = A - P = 2 - 1 = 1 \]

4. **Substitute Known Values into the Formula**: We substitute P = 1, R = 28.75, and SI = 1 into the formula:
\[ 1 = \frac{1 \times 28.75 \times T}{100} \]

5. **Rearranging the Equation to Solve for T**:
\[ 1 = \frac{28.75T}{100} \]
Multiplying both sides by 100 gives:
\[ 100 = 28.75T \]
Now, divide both sides by 28.75:
\[ T = \frac{100}{28.75} \]

6. **Calculate T**:
\[ T \approx 3.478 \]
Rounding this value gives approximately 3.47 years.

7. **Conclusion**: Therefore, the time it takes for the amount to double at an interest rate of 28.75% is approximately 3.47 years.

### Final Answer:
(b) 3.47