Final answer:
To find the annual interest rate, we use the given values in the simple interest formula I = Prt. By rearranging the equation and solving for the interest rate, we discover that the annual interest rate for the $7500 investment over 3 years is 2%.
Step-by-step explanation:
To solve for the annual interest rate using the simple interest formula I = Prt, we can plug in the values from the problem:
- I (Interest earned) = $450
- P (Principal amount) = $7500
- t (Time in years) = 3 years
Now we arrange the formula to solve for the interest rate (r):
I = Prt
$450 = $7500 × r × 3
To find 'r', divide both sides by the product of the principal and time:
r = $450 / ($7500 × 3)
r = $450 / $22500
r = 0.02
To express 'r' as a percentage, we multiply by 100:
Annual interest rate = r × 100
Annual interest rate = 0.02 × 100
Annual interest rate = 2%