To find the rate of simple interest required for a sum to double in a certain period, you can use the formula:

[ text{Simple Interest} = frac{text{Principal} times text{Rate} times text{Time}}{100} ]

In this case, you want the sum to double in 18 years, so the time (T) is 18. Let the principal be P and the rate be R. The interest is then (2P - P = P).

Now, substitute the values into the formula and solve for the rate (R):

[ P = frac{P times R times 18}{100} ]

Solving for R:

[ R = frac{100}{18} ]

Thus, the required rate of simple interest per annum is approximately 5.56%......

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Here is the answer for your question:

To find the rate of interest per annum for simple interest, we can use the formula:

[tex]\huge \boxed{SI = \frac{P\times R\times T}{100}}[/tex]

Where SI is the simple interest, P is the principal amount, R is the rate of interest per annum, and T is the time period in years.

If the principal amount is doubled in 18 years, then the simple interest is equal to the principal amount. Therefore, we can write:

[tex]\huge \boxed{P = \frac{P\times R\times 18}{100}}[/tex]

[tex]\huge \boxed{\cancel{P} = \frac{\cancel{P}\times R\times 18}{100}}[/tex]

[tex]\huge \boxed{R = \frac{100}{18}}[/tex]

[tex]\huge \boxed{\rightarrow R \approx 5.56\: percentage}[/tex]

The rate of interest when Principal is double after 18 years is "R ≈ 5.56%"

Additional information: What is SI?

SI stands for simple interest, which is the amount of money that is paid or earned on a principal amount over a fixed period of time. Simple interest is calculated by multiplying the principal amount, the rate of interest per annum, and the time period in years, and then dividing by 100. Simple interest does not take into account the interest that is added to the principal amount over time, unlike compound interest. Simple interest is often used for short-term loans or investments.

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