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To solve this problem, we will use the formula for simple interest. The key points to consider are:

1. The sum doubles in 8 years under simple interest.
2. We need to find out in how many years it will become four times the original sum at the same rate of simple interest.

### Step 1: Determine the rate of interest.
Let the principal amount (initial sum) be \( P \). After 8 years, the total amount becomes \( 2P \). 

The simple interest earned in 8 years is:
\[
2P - P = P
\]

Using the simple interest formula:
\[
\text{Simple Interest} = \frac{P \times R \times T}{100}
\]
where:
- \( P \) is the principal amount,
- \( R \) is the rate of interest,
- \( T \) is the time period in years.

Substituting the values:
\[
P = \frac{P \times R \times 8}{100}
\]
\[
R = \frac{100}{8} = 12.5\%
\]

So, the rate of interest is 12.5% per annum.

### Step 2: Find the time for the amount to become 4 times.
Now, we want the sum to become \( 4P \), which means the interest earned should be \( 3P \).

Using the simple interest formula again:
\[
3P = \frac{P \times 12.5 \times T}{100}
\]
\[
3 = \frac{12.5 \times T}{100}
\]
\[
T = \frac{3 \times 100}{12.5} = 24 \text{ years}
\]

Therefore, it will take 24 years for the sum to become four times itself.

Would you like more details or have any questions?

### Related Questions:
1. How does the formula for compound interest differ from simple interest?
2. If the rate of interest was 15%, how long would it take for the amount to double?
3. How would the result change if the sum tripled in 8 years instead of doubling?
4. What happens to the interest calculation if the interest is compounded yearly?
5. How can we graphically represent the growth of the principal over time with simple interest?

### Tip:
In simple interest, the interest amount remains the same each year because it is calculated on the original principal, unlike compound interest which accumulates.

A certain sum of money doubles itself in 8 years. In how much time it becomes 4 times of itself at the same rate of simple interest?

Learn how to calculate the time required for a sum to become four times itself under simple interest, given that it doubles in 8 years. This problem involves simple interest formula application and is suitable for students in Grades 9-11.

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