Question

At what rate percent per annum will a sum of money double in $8$ years?

• A. $12.5\%$
• B. $13.5\%$
• C. $14.5\%$
• D. $11.5\%$

Answer 1

The correct option is A

$12.5\%$

Explanation for the correct option:

Consider that sum is invested under simple interest.

The formula for the simple interest $\left(SI\right)$ is given as $SI=\frac{P\times R\times N}{100}$

Where , $P$ is the principal amount, $R$ is the percentage rate of interest per annum,$N$ is the number of years for which the sum is invested.

The amount$\left(A\right)$ is given as $A=P+SI$

According to given condition it is known that the amount is doubled.

$\Rightarrow$$A=2P$

$\Rightarrow$$2P=P+SI$

$\Rightarrow$$SI=P$

Substituting the values in the formula of simple interest we get

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

$\Rightarrow$$R=\frac{100}{8}$

$\Rightarrow$$R=12.5\%$

Thus the given amount will double in $8$ years at $12.5\%$per annum.

Hence, option$\left(A\right)$ i.e. $12.5\%$ is the correct answer.