Question

Hayden invested $200 in a savings account that earned 3.3% simple interest each year. William invested $300 in a savings account that earned 2.5% simple interest each year. Neither Hayden nor William add or take out money from their accounts. Hayden claims that she will earn more interest on her account than William after 2 years because she has a greater interest rate. Do you agree with Hayden? Why or why not? Be sure to defend your answer with numbers.

Answer 1

Despite Hayden's higher interest rate, William will earn more interest after 2 years because he invested a larger principal amount. Hayden will earn $13.20, while William will earn $15.00.

Step-by-step explanation:

To determine whether Hayden will earn more interest than William, we need to calculate the simple interest for each investment over 2 years. The formula for simple interest is I = P x r x t, where I is the interest earned, P is the principal amount invested, r is the annual interest rate (expressed as a decimal), and t is the time in years.

For Hayden, the interest earned after 2 years can be calculated as:

I = $200 x 0.033 x 2 = $13.20

For William, the interest earned after 2 years can be calculated as:

I = $300 x 0.025 x 2 = $15.00

Based on these calculations, William will have earned more interest ($15) on his account compared to Hayden ($13.20) after 2 years, despite Hayden having a greater interest rate. This is because William's principal amount was larger.