Chapter 7.7, Problem 36HP

To determine

To calculate: The length of time.

Answer to Problem 36HP

The length of time is 10 years.

Explanation of Solution

Given information: The principal amount is $100. Rate of simple interest is 10%. The amount will be doubled.

Formula used: The simple interest formula is $S.I=P\times r\times t$

Where, S.I = simple interest amount, P = principal amount, r =annual rate of interest, t = the length of time the money is invested.

Calculation:

In the problem given,

P = $100, r = $10\%=\frac{10}{100}=0.1$ , $A=P+S.I$ =$ $(2\times 100)$ =$200

  $S.I=A-P$ =$ $(200-100)$ =$100

  $\begin{array}{l}S.I=P\times r\times t\\ \Rightarrow 100=100\times 0.1\times t\\ \Rightarrow 100\times 0.1\times t=100\\ \Rightarrow 10t=100\\ \Rightarrow t=\frac{100}{10}\\ \Rightarrow t=10\end{array}$

So, the length of time is 10 years.