The rate per cent per annum at which the sum of money double itself in 16 yr at simple interest is

Options

A. `6(1)/3%`
B. `6(1)/4%`
C. `6(1)/2%`
D. `6(1)/5%`

Answer

To find the rate per cent per annum at which a sum of money doubles itself in 16 years at simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the rate of interest (R) when a principal amount (P) doubles in 16 years.

2. **Assume a Principal Amount**: Let's assume the principal amount (P) is 100. Therefore, the amount (A) after 16 years will be 200 (since it doubles).

3. **Calculate the Simple Interest (SI)**:
\[ \text{Simple Interest (SI)} = \text{Amount} - \text{Principal} = 200 - 100 = 100 \]

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

5. **Substitute the Known Values**: We know SI = 100, P = 100, and T = 16. Substitute these values into the formula:
\[ 100 = \frac{100 \times R \times 16}{100} \]

6. **Simplify the Equation**: The 100 in the numerator and denominator cancels out:
\[ 100 = R \times 16 \]

7. **Solve for R**: Now, divide both sides by 16 to find R:
\[ R = \frac{100}{16} \]

8. **Calculate R**: Simplifying \( \frac{100}{16} \):
\[ R = 6.25 \]

9. **Convert to Percentage**: Since R is already in percentage form, we can express it as:
\[ R = 6 \frac{1}{4}\% \]

### Final Answer:
The rate per cent per annum at which the sum of money doubles itself in 16 years at simple interest is \( 6 \frac{1}{4}\% \).