Simple Interest Calculation: Doubling Time

This solution explains how to find the number of years required for an amount of money to double at a specific simple interest rate.

Understanding Simple Interest Doubling

When an amount of money doubles, the simple interest earned is exactly equal to the initial principal amount.

• Let the Principal amount be \( P \).
• The final Amount becomes \( 2P \).
• Thus, the Simple Interest (SI) earned is \( SI = 2P - P = P \).

Applying the Simple Interest Formula

The standard formula for calculating Simple Interest is:

$ SI = \frac{P \times R \times T}{100} $

Where:

• \( SI \) = Simple Interest
• \( P \) = Principal Amount
• \( R \) = Annual Rate of Interest (in %)
• \( T \) = Time (in years)

Calculating Time for Money to Double

From the question, we have:

• Rate (\( R \)) = \( 6 \frac{1}{4}\% \). This can be written as \( 6.25\% \).
• For the amount to double, we know \( SI = P \).

Substitute these values into the simple interest formula:

$ P = \frac{P \times 6.25 \times T}{100} $

To find the time (\( T \)), we solve the equation:

Divide both sides by \( P \) (assuming \( P \neq 0 \)):

$ 1 = \frac{6.25 \times T}{100} $

Rearrange to isolate \( T \):

$ T = \frac{100}{6.25} $

Calculate the value of \( T \):

$ T = \frac{10000}{625} $

$ T = 16 $

Conclusion: Time to Double

Therefore, it takes 16 years for an amount of money to double itself with a simple interest rate of \( 6 \frac{1}{4}\% \) per annum.