Final answer:
To determine the annual interest rate, we use the simple interest formula I=PRT and the information that the interest difference over 2 years is $24. The rate is then calculated to be 0.02 or 2%.
Step-by-step explanation:
The student is asking how to find the annual interest rate for a simple interest account given the interest earned over different periods of time. To solve this, we will use the formula for simple interest, which is I = PRT (Interest = Principal × Rate × Time). The question tells us that the difference in interest earned after 5 years and after 3 years is $24.
Let's denote the unknown annual interest rate as 'r'. Using the simple interest formula for 5 years we get:
I_5 = P × r × 5
And for 3 years:
I_3 = P × r × 3
The difference between the two is:
I_5 - I_3 = P × r × 5 - P × r × 3 = P × r × (5 - 3) = P × r × 2
So, we know that:
P × r × 2 = $24, and Principal (P) is given as $600.
Substituting the values we get:
$600 × r × 2 = $24
From this equation we can solve for 'r':
r = $24 / ($600 × 2) = $24 / $1200 = 0.02
Therefore, the annual interest rate is 2%.