Final answer:
Using the simple interest formula I = Prt, and rearranging it to solve for the annual interest rate (r), we calculate that an investment of $7,500 earning $450 over 3 years has an annual interest rate of 2%.
Step-by-step explanation:
To solve the given problem, we want to find the annual interest rate when an investment of $7,500 earns $450 over 3 years. We use the simple interest formula I = Prt, where I is the interest earned, P is the principal amount invested, r is the annual interest rate, and t is the time in years. In this case, we have
- I = $450
- P = $7,500
- t = 3 years
We want to find r. We can rearrange the formula to solve for r as follows:
r = I / (Pt)
So, r = $450 / ($7,500 × 3)
When we calculate this, r = $450 / $22,500 = 0.02
To express r as a percentage, we multiply by 100:
r × 100 = 0.02 × 100 = 2%
Therefore, the annual interest rate is 2%.