Question

the formula for simple interest, i, is $i = prt$ where $p$ is the principal, $r$ is the annual interest rate, and $t$ is the time elapsed in years. solve the formula for $r$. use the equation you just found to determine the annual interest rate on an account that earned $45.00 in simple interest after 6 months with a principal deposit of $3,000.00.

Explanation:

Step1: Solve for \( r \)

We start with the simple interest formula \( I = Prt \). To solve for \( r \), we divide both sides of the equation by \( Pt \) (assuming \( P
eq 0 \) and \( t
eq 0 \)). So we get \( r=\frac{I}{Pt} \).

Step2: Substitute values

First, we need to convert the time from months to years. Since 6 months is \( \frac{6}{12} = 0.5 \) years. Now we substitute \( I = 45 \), \( P = 3000 \), and \( t = 0.5 \) into the formula for \( r \). So \( r=\frac{45}{3000\times0.5} \).

Step3: Calculate the value

First, calculate the denominator: \( 3000\times0.5 = 1500 \). Then, \( r=\frac{45}{1500}=0.03 \), which is \( 3\% \) when expressed as a percentage.

Answer:

The formula for \( r \) is \( r = \frac{I}{Pt} \), and the annual interest rate is \( 3\% \) (or \( 0.03 \) in decimal form).