Solve the following question.

An investment grows to 2.5 times its original principal amount over a period of 10 years at a constant simple interest rate. Calculate the annual rate of interest.

The correct option is 15%.

Step 1: Understand the given data

Let the original principal amount be $P$.

According to the question, the total amount ($A$) after 10 years grows to 2.5 times the principal amount.

$A=2.5P$

Time period ($T$) = 10 years.

Step 2: Calculate the Simple Interest (SI)

Simple interest earned is the difference between the total amount and the principal amount:

$SI=A-P$

Substituting $A=2.5P$ into the formula:

$SI=2.5P-P=1.5P$

Step 3: Calculate the annual rate of interest ($R$)

Using the standard formula for Simple Interest:

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

Substitute the known values ($SI=1.5P$ and $T=10$) into the equation:

$1.5P=\frac{10\times P\times R}{100}$

Divide both sides of the equation by $P$:

$1.5=\frac{10R}{100}$

Simplify the fraction on the right side:

$1.5=\frac{R}{10}$

Multiply both sides by 10 to solve for $R$:

$R=1.5\times 10=15$

Thus, the annual rate of interest is 15%.