A sum of money will double itself in 16 years at simple interest with yearly rate of-

Options

A. `10%`
B. `6 1/4%`
C. `8%`
D. `16%`

Answer

To solve the problem of finding the yearly rate at which a sum of money will double 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 simple interest that allows a sum of money to double in 16 years.

2. **Define the Variables**:
- Let the principal amount (initial sum of money) be \( P = 100 \) (for simplicity).
- The amount after 16 years will be \( A = 200 \) (since it doubles).
- The time period \( T = 16 \) years.

3. **Calculate the Simple Interest (SI)**:
- The simple interest earned over the time period can be calculated as:
\[ SI = A - P = 200 - 100 = 100 \]

4. **Use the Simple Interest Formula**:
- The formula for simple interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
- Where \( R \) is the rate of interest per annum.

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 \( R \)**:
- Divide both sides by 16 to find \( R \):
\[ R = \frac{100}{16} = 6.25 \]

8. **Convert to Percentage**:
- The rate \( R = 6.25\% \).

### Final Answer:
The yearly rate of simple interest is **6.25%**.