Chapter 7.7, Problem 27E

To determine

To find: the time in which the principal amount gets doubled at the rate $r=10\%\text{simple}\text{annual}\text{interest}$ and explain.

Answer to Problem 27E

The Principal amount gets doubled in $10\text{years}$

Explanation of Solution

Given information: A principal amount gets doubled at a rate $r=10\%\text{simple}\text{annual}\text{interest}$

Concept Used:

Simple interest problem requires the use of the following formula:

  $\begin{array}{l}I=Prt\\ A=P+I\end{array}$

Calculation:

As per the given problem

Principal amount gets doubled at a rate $r=10\%\text{simple}\text{annual}\text{interest}$

Let the amount is $P$ and gets doubled $2P$ in time $t$

Therefore,

  $\begin{array}{l}A=P+I\\ 2P=P+I\\ I=2P-P\\ I=P\end{array}$

Substitute the values in the formula

  $\begin{array}{l}I=Prt\\ \Rightarrow P=P\times \frac{10}{100}\times t\\ \Rightarrow t=10\end{array}$

The Principal amount gets doubled in $10\text{years}$

The account will double when the interest earned equals the principal. As the principal amount gets equal to the interest this will be possible when the time will $10\text{years}$ .

Conclusion:

The Principal amount gets doubled in $10\text{years}$ .

The account will double when the interest earned equals the principal. As the principal amount gets equal to the interest this will be possible when the time will $10\text{years}$ .