Chapter 6.1, Problem 33E

To determine

To calculate: The equivalent rate.

Answer to Problem 33E

The equivalent rate is $\$2750$ per month.

Explanation of Solution

Given information:

The following equivalent fractions:

  $\frac{\$33,000}{\text{1 year}}=\frac{?\text{ dollars}}{1\text{ month}}$

Calculation:

To find an equivalent rate, convert from dollars per year to dollars per month. To do so, multiply the rate by a conversion factor. There are $12$ months in $1$ year, so $\frac{\text{1 year}}{\text{12 months}}=1$ .

  $\begin{array}{l}\frac{\$33,000}{\text{1 year}}\\ \Rightarrow \frac{\$33,000}{\text{1 year}}\times \frac{\text{1 year}}{\text{12 months}} \left[\text{Multiply rate by common conversion factor}\right]\\ \Rightarrow \frac{\$\stackrel{2750}{\cancel{33,000}}}{\text{1 }\cancel{\text{year}}}\times \frac{\text{1 }\cancel{\text{year}}}{\cancel{\underset{1}{12}}\text{months}} \left[\text{Divide out common factor and unit}\right]\\ \Rightarrow \frac{\text{\$2750 }}{1\text{ month}} \left[\text{Simplify}\right]\end{array}$ Therefore, the equivalent rate is $\$2750$ per month.