Question

1. analyze and persevere keyon earned $76.00 in interest after 5 years on a principal of $400. jane earned $82.00 in interest after 2 years on a principal of $1,000. which bank would you rather use, keyons or janes? why?

Explanation:

Step1: Calculate Keyon's interest rate

Use the simple - interest formula \(I = Prt\), where \(I\) is interest, \(P\) is principal, \(r\) is rate, and \(t\) is time. Rearranging for \(r\), we get \(r=\frac{I}{Pt}\).
For Keyon, \(I = 76\), \(P = 400\), \(t = 5\).
\(r_{Keyon}=\frac{76}{400\times5}=\frac{76}{2000}=0.038 = 3.8\%\)

Step2: Calculate Jane's interest rate

For Jane, \(I = 82\), \(P = 1000\), \(t = 2\).
Using \(r=\frac{I}{Pt}\), \(r_{Jane}=\frac{82}{1000\times2}=\frac{82}{2000}=0.041=4.1\%\)

Answer:

I would rather use Jane's bank. Because Jane's interest rate (\(4.1\%\)) is higher than Keyon's (\(3.8\%\)). A higher interest rate means more interest earned on the principal amount over time.