Simple Interest Rate Calculation

The problem asks for the annual simple interest rate (R) when a sum of money becomes 5 times itself in 15 years.

Understanding Simple Interest

Let the principal amount be P.

The amount becomes 5 times, so the final Amount (A) = 5P.

The Simple Interest (SI) earned is the difference between the Amount and the Principal:

SI = A - P = 5P - P = 4P

The time period (T) is given as 15 years.

Applying the Simple Interest Formula

The formula for Simple Interest is:

\begin{equation} SI = \frac{P \times R \times T}{100} \end{equation}

We know SI = 4P and T = 15 years. Substitute these values into the formula:

\begin{equation} 4P = \frac{P \times R \times 15}{100} \end{equation}

Solving for the Rate (R)

Divide both sides by P (assuming P ≠ 0):

\begin{equation} 4 = \frac{R \times 15}{100} \end{equation}

Rearrange the equation to solve for R:

\begin{equation} R = \frac{4 \times 100}{15} \end{equation}

\begin{equation} R = \frac{400}{15} \end{equation}

Calculate the value:

\begin{equation} R = \frac{80}{3} \approx 26.666... \end{equation}

Rounding to two decimal places, the rate is 26.67%.

Final Answer

The required simple interest rate is 26.67% per year.