Q15. - Algebra 2

Question

Use the following information.

Simple interest is calculated using the formula $I=prt$, where p represents the principal in dollars, $r$ represents the annual interest rate, and $t$ represents the time in years. Find the simple interest $I$ given each of the following values.

 $p=\$31,000, r=2\frac{1}{2}\%, t=18 months$

Step-by-Step Solution

Answer

Simple interest is $I=\$1,162.5$ 

Step 1 - Meaning of given formula I = p r t

$prt$ implies product of principle value, annual interest rate and time 

So, interest rate can be evaluated by multiplying these three values

Step 2 - Substitute given values

Convert 18 months into years by dividing 18 by 12

 $18÷12=1.5$

Substitute $\$31,000$ for $p$, $2\frac{1}{2}\%$ for $r$ and $1.5$ for $t$ into given expression

$I=31000\times 2\frac{1}{2}\%\times 1.5$ 

 

Step 3 - Simplify 31000 × 2 1 2 % × 1 . 5

Substitute $\frac{2.5}{100}$ for  $2\frac{1}{2}\%$

 $\begin{array}{c}I=31000\times \frac{2.5}{100}\times 1.5\\ =\frac{116250}{100}\\ =1162.5\end{array}$

Thus, simple interest is  $I=\$1,162.5$