Simple Interest Rate Calculation

The question asks for the annual interest rate required for a sum of money to become five times its original value in 4 years under simple interest.

Given Information:

• Time period ($T$) = 4 years
• The final amount is 5 times the principal sum.

Calculating Simple Interest (SI):

Let the principal sum be $P$. The final amount ($A$) becomes $5P$. The Simple Interest earned is the difference between the final amount and the principal:

$SI = A - P$

Substituting the values:

$SI = 5P - P = 4P$

Finding the Rate (R):

The formula for Simple Interest is:

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

Now, substitute the known values ($SI = 4P$ and $T = 4$ years) into the formula:

$4P = \frac{P \times R \times 4}{100}$

To solve for R, we can simplify the equation. Divide both sides by $P$ (assuming $P \neq 0$):

$4 = \frac{R \times 4}{100}$

Multiply both sides by 100:

$4 \times 100 = R \times 4$

$400 = 4R$

Divide both sides by 4:

$R = \frac{400}{4}$

$R = 100$

Therefore, the rate per annum is 100%.