Chapter 9.7, Problem 5PPS

To determine

How many people will own a computer in2015

Answer to Problem 5PPS

The number of people will own a computer in 2015 is $885\text{million}$

Explanation of Solution

Given information:

The number of people who own computers has increased 23.2% annually since 1990 and if half million people owned computer in 1990

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
  $\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To find how many people own a computer in 2015

  $\begin{array}{c}A=\frac{1}{2}\text{million}\\ r=\text{23}\text{.2\%}\\ \text{=}\frac{23.2}{100}\\ =0.232\\ t=25\end{array}$

  $\begin{array}{l}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ A=\frac{1}{2}{\left(1+0.232\right)}^{25}\\ A=\frac{1}{2}{\left(1.0232\right)}^{25}\\ =\frac{1}{2}\times 1.77\\ A=0.885\end{array}$

Thus, the number of people will own a computer in 2015 is $885\text{million}$