Question

A sum becomes five times of itself in 8 years at simple interest. What is the rate of interest per annum?

• A. 37.5%
• B. 25%
• C. 62.5%
• D. 50%

Answer 1

Answer:

D. 50%

1. Identify the given information:

• Let the Principal amount be $P$.

• The sum becomes five times itself, so the Amount ($A$) is $5P$.

• Time ($T$) = $8$ years.

2. Calculate the Simple Interest ($SI$):

The formula for Simple Interest is:

$SI = A - P$

Substituting the values:

$SI = 5P - P = 4P$

3. Use the Simple Interest formula to find the Rate ($R$):

The formula for Simple Interest is also:

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

Substitute the known values into the equation:

$4P = \frac{P \times R \times 8}{100}$

Since $P$ is on both sides (and $P \neq 0$), we can cancel it out:

$4 = \frac{R \times 8}{100}$

Now, solve for $R$:

$4 \times 100 = 8R$

$400 = 8R$

$R = \frac{400}{8}$

$R = 50\%$

Final Answer:

The rate of interest per annum is $50\%$.