Question

At what rate of simple interest a certain sum will be doubled in $10$ years?
(A) $10\;\% $
(B) $12\;\% $
(C) $13\;\% $
(D) $15\;\% $

Answer 1

Hint: In the solution we will use the simple interest formula and concept. When any question will be asking about the rate of simple interest or principal amount or time then simply put the given values in the simple interest formula and see which unknown variable will be required to find out.

Complete step by step solution:
The number of years is $10\;{\rm{years}}$.

Let us assume that the principal amount is $P$.

Now express the formula of total amount.
$A = P + SI$

Here,
$P$is the principal amount.
$A$ is the total amount.
$SI$ is the simple interest.

Since, it is given that the sum will be doubled in $10$ years. It means that the amount after $10$ years will be equal to $2P$.

Substitute $2P$for $A$ in above expression to obtain the simple interest.
$\begin{array}{c}
2P = P + SI\\
SI = P
\end{array}$

The formula of simple interest is given as.
$SI = \dfrac{{PRT}}{{100}}$

Here,
$P$is the principal amount.
$R$ is the interest rate.
$T$ is the time.

Substitute $P$ for $SI$ and $10\;{\rm{years}}$ for $T$ in above expression to obtain the rate.
$\begin{array}{c}
P = \dfrac{{P \times R \times 10\;{\rm{years}}}}{{100}}\\
R = 10\;\%
\end{array}$

Therefore, the correct answer is $10\;\% $ that is option (A).

Note: In this type of questions, make sure that the total amount will be doubled but not the principal amount. This is the only tricky part of the question.