Question

You invest \(\$ 80\) at a simple annual interest rate of \(2 \%\). How much simple interest would you earn in 1.5 years? Use unit analysis to check the units in your response.

Short answer

The simple interest earned would be $2.4.

Step-by-step solution

Understand Simple Interest

First, understand what simple interest is: it is interest calculated on the original principal only. You can calculate simple interest using this formula: \(I = PRT\), where: \(I\) is the interest, \(P\) is the principal (the initial amount of money), \(R\) is the rate of interest per period, and \(T\) is the time the money is invested for, in years.

Substitute Values into the Formula

Substitute the given values into the formula. Here, \(P = $80\), \(R = 2% = 0.02\) (as percent means per hundred, we divide the given number by 100 to convert it into decimal form), \(T = 1.5\) years. We find that \(I = 80 * 0.02 * 1.5\).

Calculate the Result

Perform the multiplication to calculate the interest. This gives us \(I = $2.4\).

Perform Unit Analysis

For unit analysis, ensure that your final answer is in the correct units. In this case, the question asks for the interest in dollars, so you should present your answer in dollars. The result from step 3 is already in the correct unit.