Simple interest uses the formula:
I = prt
where p = the initial principal,
r = the interest rate per unit time
t = time in the units used to express the interest rate.
Your time unit is "year", and the interest rate is annual interest (per year).
Simple interest does not include adding the interest each year. In other words it is not "compound interest". That would make the formula more complex and a little more difficult to solve.
The banker's rule would not apply here. It specifies that the time should be the exact fraction of a year for the time of a loan. (The equation for the interest is the same for a loan or an investment. The only difference is which side of the "loan" you're on.) Your problem states that the time is 3 years, which is just a number of whole years.
The interest to be earned in 3 years is:
4500 - 3200 = 1300
Plug the known values into I = prt and solve for r:
1300 = 3200 * r * 3
1300 = 9600 * r
r = 1300 / 9600
r = 0.1354 = 13.54%
I hope Micheal is patient! He'll probably need more than 3 years!