Question

1. higher order thinking theodore earned $92.40 in interest after 4 years on a principal of $550. bella earned $216.00 in interest after 4 years on a principal of $1,500. which bank would you rather use, theodore’s or bella’s? explain.

Explanation:

Step1: Calculate Theodore's interest rate

The simple - interest formula is \(I = Prt\), where \(I\) is the interest, \(P\) is the principal, \(r\) is the rate of interest, and \(t\) is the time.
We know that for Theodore, \(I=\$92.40\), \(P = \$550\), and \(t = 4\) years.
We need to solve for \(r\). Rearranging the formula \(r=\frac{I}{Pt}\).
Substitute the values: \(r=\frac{92.40}{550\times4}\).
First, calculate \(550\times4=2200\).
Then \(r=\frac{92.40}{2200}=0.042 = 4.2\%\).

Step2: Calculate Bella's interest rate

For Bella, \(I = \$216\), \(P=\$1500\), and \(t = 4\) years.
Using the formula \(r=\frac{I}{Pt}\).
Substitute the values: \(r=\frac{216}{1500\times4}\).
First, calculate \(1500\times4 = 6000\).
Then \(r=\frac{216}{6000}=0.036=3.6\%\).

Answer:

I would rather use Theodore's bank. Since Theodore's bank has an interest rate of \(4.2\%\) and Bella's bank has an interest rate of \(3.6\%\), and a higher interest rate means more interest earned on the same amount of principal over the same period of time.