Question

If the sum double itself in 2 years, find the rate % per annum​

Answer 1

• As per the given data in the question, we have to find the amount.
• Given data- The sum is double itself in $2$ years.
• To find- Rate $\%$ per annum.
• We will apply the compound interest formula.

• When the interest is added to the principal(P) with a given rate(r) at the end of each year(n), as we say the interest is compounded annually, then the amount is calculated as follows.
• $A=P\left ( 1+\frac{r}{100} \right )^{^{n}}$

• Then, we will substitute,

         $\Rightarrow 2P=(1+r)^{2}$

         $\Rightarrow r=\sqrt{2}-1$

         $\Rightarrow r= 0.414\\\Rightarrow r=41.4\%$

         Hence, the rate per annum will be $41.4\%.$

Answer 2

As per data given in the question,

We have to determine the value of rate percentage.

We know that,

Rate percent is nothing but a rate on which money is borrowed for a certain span of time.

From the data,

It is given that:- The sum is doubled itself in 2 years,

To find - $Rate \%$ per annum,

As we know that,

The formula for amount,

$A=P\left(1+\frac{r}{n}\right)^{2}$

Now, substitute the given values we get

$\begin{array}{l}=>2 P=P(1+r)^{2} \\=>r=\sqrt{2}-1 \\=>0.414 \\=>41.4 \%\end{array}$

Hence, The $rate \%$ per annum is $41.4 \%$